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  • 1
    Digitale Medien
    Digitale Medien
    Unsteady convection and convection-diffusion problems via direct overlapping domain decomposition methods (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 387-406 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In solving unsteady problems,domain decomposition methods may be used either for iterative preconditioning each global implicit time-step or directly (noniteratively) within a blockwise implicit time-stepping procedure, in the latter case, the inner boundary values for the subproblems are generated by explicit time-extrapolation. The overlapping variants of this method have been proved to be efficient tools for solving parabolic and first-order hyperbolic problems on modern parallel computers, because they require global communication only once per time-step. The mechanism making this possible is the exponential decay in space of the time-discrete Green's function. We investigate several model problems of convection and convection-diffusion. Favorable optimal and far-reaching estimates of the overlap required have been established in the case of exemplary standard upwind finite-difference schemes. In particular, it has been shown that the overlap for the convection-diffusion problem is the additive function of overlaps for the corresponding convection and diffusion problem to be considered independently. These results have been confirmed with several numerical test examples. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 387-406, 1998
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    A first-second order splitting method for a third-order partial differential equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 89-96 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element method ; third-order differential equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89-96, 1998
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  • 3
    Digitale Medien
    Digitale Medien
    Galerkin discontinuous approximation of the transport equation and viscoelastic fluid flow on quadrilaterals (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 97-114 
    Details
    ISSN: 0749-159X
    Schlagwort(e): non-Newtonian fluids ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Numerical simulation of industrial processes involving viscoelastic liquids is often based on finite element methods on quadrilateral meshes. However, numerical analysis of these methods has so far been limited to triangular meshes. In this work, we consider quadrilateral meshes. We first study the approximation of the transport equation by a Galerkin discontinuous method and prove an O(hk+1/2) error estimates for the Qk finite element. Then we study a differential model for viscoelastic flow with unknowns u the velocity, p the pressure, and σ the viscoelastic part of the extra-stress tensor. The approximations are ((Q1)2 transforms of) Qk+1 continuous for u, Qk discontinuous for σ, and Pk discontinuous for p, with k ≥ 1. Upwinding for σ is obtained by the Galerkin discontinuous method. We show that an error estimate of order O(hk+1/2) is valid in the energy norm for the three unknowns. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 97-114, 1998
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  • 4
    Digitale Medien
    Digitale Medien
    Stabilized spectral element approximation for the Navier-Stokes equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 115-141 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Navier-Stokes equations ; spectral elements ; stabilization techniques ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The conforming spectral element methods are applied to solve the linearized Navier-Stokes equations by the help of stabilization techniques like those applied for finite elements. The stability and convergence analysis is carried out and essential numerical results are presented demonstrating the high accuracy of the method as well as its robustness. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 115-141, 1998
    Zusätzliches Material: 11 Ill.
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  • 5
    Digitale Medien
    Digitale Medien
    Spectral approximation in the numerical stability study of nondivergent viscous flows on a sphere (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 143-157 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Normal mode stability ; spectral approximation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The accuracy of calculating the normal modes in the numerical linear stability study of two-dimensional nondivergent viscous flows on a rotating sphere is analyzed. Discrete spectral problems are obtained by truncating Fourier's series of the spherical harmonics for both the basic flow and the disturbances to spherical polynomials of degrees K and N, respectively. The spectral theory for the closed operators [1], and embedding theorems for the Hilbert and Banach spaces of smooth functions on a sphere are used to estimate the rate of convergence of the eigenvalues and eigenvectors. It is shown that the convergence takes place if the basic state is sufficiently smooth, and the truncation numbers K and N of Fourier's series for the basic flow and disturbances tend to infinity keeping the ratio N/K fixed. The convergence rate increases with the smoothness of the basic flow and with the power s of the Laplace operator in the vorticity equation diffusion term. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:143-157, 1998
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  • 6
    Digitale Medien
    Digitale Medien
    A second-order ADI scheme for three-dimensional parabolic differential equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 159-168 
    Details
    ISSN: 0749-159X
    Schlagwort(e): ADI scheme ; parabolic differential equation ; stability ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A second-order unconditionally stable ADI scheme has been developed for solving three-dimensional parabolic equations. This scheme reduces three-dimensional problems to a succession of one-dimensional problems. Further, the scheme is suitable for simulating fast transient phenomena. Numerical examples show that the scheme gives an accurate solution for the parabolic equation and converges rapidly to the steady state solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:159-168, 1998
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 297-315 
    Details
    ISSN: 0749-159X
    Schlagwort(e): elasticity equations ; least-squares ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stage least-squares finite element procedure is introduced for approximating the solution to this system with appropriate boundary conditions. It is shown that the two-stage least-squares scheme is stable and, with respect to the order of approximation for smooth exact solutions, the rates of convergence of the approximations for all the unknowns are optimal both in the H1-norm and in the L2-norm. Numerical experiments with various values of the parameter are examined, which demonstrate the theoretical estimates. Among other things, computational results indicate that the behavior of convergence is uniform in the nonnegative parameter. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 297-315, 1998
    Zusätzliches Material: 4 Tab.
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  • 8
    Digitale Medien
    Digitale Medien
    Monotone iterations for numerical solutions of reaction-diffusion-convection equations with time delay (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 339-351 
    Details
    ISSN: 0749-159X
    Schlagwort(e): monotone iteration ; finite difference equation ; reaction-diffusion-convection ; time delay ; upper and lower solutions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article we use the monotone method for the computation of numerical solutions of a nonlinear reaction-diffusion-convection problem with time delay. Three monotone iteration processes for a suitably formulated finite-difference system of the problem are presented. It is shown that the sequence of iteration from each of these iterative schemes converges from either above or below to a unique solution of the finite-difference system without any monotone condition on the nonlinear reaction function. An analytical comparison result among the three processes of iterations is given. Also given is the application of the iterative schemes to some model problems in population dynamics, including numerical results of a model problem with known analytical solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 339-351, 1998
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    A numerical method for the first-order wave equation with discontinuous initial data (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 353-365 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Euler equations ; contact discontinuity ; finite difference schemes ; dispersion ; first-order wave equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We introduce a method, constructed such that numerical solutions of the wave equation are well behaved when the solutions also contain discontinuities. The wave equation serves as a model problem for the Euler equations when the solution contains a contact discontinuity. Numerical computations of linear equations and the Euler equations in one and two dimensions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 353-365, 1998
    Zusätzliches Material: 4 Ill.
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  • 10
    Digitale Medien
    Digitale Medien
    Superconvergence in the projected-shear plate-bending finite element method (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 367-386 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element methods ; superconvergence ; the Reissner-Mindlin plate ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A projected-shear finite element method for periodic Reissner-Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L2-norm, the H1-norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justified in some weak senses. All the convergence and superconvergence results are uniform with respect to the thickness parameter t. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 367-386, 1998
    Zusätzliches Material: 1 Ill.
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  • 11
    Digitale Medien
    Digitale Medien
    Global and domain-decomposed mixed methods for the solution of Maxwell's equations with application to magnetotellurics (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 407-437 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Maxwell's equations ; magnetotellurics ; domain decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A collection of global and domain decomposition mixed finite element schemes for the approximate solution of the harmonic Maxwell's equations on a bounded domain with absorbing boundary conditions at the artificial boundaries are presented. The numerical procedures allow us to solve efficiently the direct problem in magnetotellurics consisting of determining the electromagnetic scattered field in a two-dimensional earth model of arbitrary conductivity properties. Convergence results for the numerical procedures are derived. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 407-437, 1998
    Zusätzliches Material: 1 Ill.
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  • 12
    Digitale Medien
    Digitale Medien
    The coupling of boundary integral and finite element methods for the nonstationary exterior flow (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 549-565 
    Details
    ISSN: 0749-159X
    Schlagwort(e): boundary integral ; finite element ; Navier-Stokes equations ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we represent a new numerical method for solving the nonstationary Navier-Stokes equations in an unbounded domain. The technique consists of coupling the boundary integral and the finite element method. The variational formulation and the well-posedness of the coupling method are obtained. The convergence and optimal error estimates for the approximate solution are provided. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 549-565, 1998
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  • 13
    Digitale Medien
    Digitale Medien
    Numerical analysis of finite element methods for miscible displacements in porous media (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 519-548 
    Details
    ISSN: 0749-159X
    Schlagwort(e): miscible displacements ; finite elements ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time-stepping algorithm that uncouples the system at each time-step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post-processing technique involving the conservation of mass and Darcy's law. A stabilized finite element (SUPG) method is applied to the convection-diffusion equation delivering stable and accurate solutions. Error estimates with quasi-optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post-processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 519-548, 1998
    Zusätzliches Material: 6 Ill.
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  • 14
    Digitale Medien
    Digitale Medien
    Finite differences on triangular grids (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 567-579 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite difference ; finite element ; triangular grid ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We define a finite differences method for triangular grids and we show how to link it to a finite element method. From this new point of view we then analyze properties of the solution and convergence. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 567-579, 1998
    Zusätzliches Material: 5 Ill.
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  • 15
    Digitale Medien
    Digitale Medien
    Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 593-606 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite difference approximations ; Poisson equation ; symbolic computation ; Mathematica ; three-dimensions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourth-order finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 593-606, 1998
    Zusätzliches Material: 1 Ill.
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  • 16
    Digitale Medien
    Digitale Medien
    Applications of a space decomposition method to linear and nonlinear elliptic problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 717-737 
    Details
    ISSN: 0749-159X
    Schlagwort(e): parallel ; domain decomposition ; nonlinear ; elliptic equation ; space decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This work presents some space decomposition algorithms for a convex minimization problem. The algorithms has linear rate of convergence and the rate of convergence depends only on four constants. The space decomposition could be a multigrid or domain decomposition method. We explain the detailed procedure to implement our algorithms for a two-level overlapping domain decomposition method and estimate the needed constants. Numerical tests are reported for linear as well as nonlinear elliptic problems. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 717-737, 1998
    Zusätzliches Material: 7 Ill.
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  • 17
    Digitale Medien
    Digitale Medien
    A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 695-716 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Rosenau equation ; orthogonal spline collocation method ; differential algebraic equations (DAEs) ; implicit Runge-Kutta methods ; decay estimates ; BBM (Benjamin-Bona-Mahony) equation ; BBMB (Benjamin-Bona-Mahony-Burgers) equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A second-order splitting method is applied to a KdV-like Rosenau equation in one space variable. Then an orthogonal cubic spline collocation procedure is employed to approximate the resulting system. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index 1. Error estimates in L2 and L∞ norms have been obtained for the semidiscrete approximations. For the temporal discretization, the time integrator RADAU5 is used for the resulting system. Some numerical experiments have been conducted to validate the theoretical results and to confirm the qualitative behaviors of the Rosenau equation. Finally, orthogonal cubic spline collocation method is directly applied to BBM (Benjamin-Bona-Mahony) and BBMB (Benjamin-Bona-Mahony-Burgers) equations and the well-known decay estimates are demonstrated for the computed solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 695-716, 1998
    Zusätzliches Material: 9 Ill.
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  • 18
    Digitale Medien
    Digitale Medien
    On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 781-814 
    Details
    ISSN: 0749-159X
    Schlagwort(e): hyperbolic problems ; IBVP ; multi-dimensional ; nonorthogonal mesh ; quasi-linear form ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 781-814, 1998
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  • 19
    Digitale Medien
    Digitale Medien
    A finite difference scheme for traveling wave solutions to Burgers equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 815-820 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Burgers equation ; nonstandard finite difference schemes ; traveling waves ; exact solutions ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We construct a finite difference scheme for the ordinary differential equation describing the traveling wave solutions to the Burgers equation. This difference equation has the property that its solution can be calculated. Our procedure for determining this solution follows closely the analysis used to obtain the traveling wave solutions to the original ordinary differential equation. The finite difference scheme follows directly from application of the nonstandard rules proposed by Mickens. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 815-820, 1998
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  • 20
    Digitale Medien
    Digitale Medien
    A model of a homogenized cavity corresponding to a multinozzle droplet generator for continuous ink-jet printers (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 821-842 
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    ISSN: 0749-159X
    Schlagwort(e): homogenization ; asymptotic analysis ; ink-jet printer ; droplet generator ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We modelize the behavior of a vibrating fluid cavity. Small nozzles are uniformly distributed in one direction on a side of the cavity. By means of asymptotic expansion in powers of the smallest dimension of the cavity, including boundary layer terms, we get the convergence of the solution of the three-dimensional problem, as well as the convergence of the solution of the “homogenized” three-dimensional problem towards the solution of the same two-dimensional problem. Numerical experiments have been carried out in order to illustrate the previous theoretical results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 821-842, 1998
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  • 21
    Digitale Medien
    Digitale Medien
    Approximation to a parabolic system modeling the thermoelastic contacts of two rods (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 1-25 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Finite difference ; thermoelastic contact ; nonlinear parabolic system ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that may come into contact as a result of thermoelastic expansion. We construct the approximate solutions based on a set of finite difference schemes to the system, and we will prove that the approximate solutions converge strongly to the exact solutions. Moreover, we obtain and prove rigorously the error bound, which measures the difference between the exact solutions and approximate solutions in a reasonable norm. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 1-25, 1998
    Zusätzliches Material: 3 Ill.
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  • 22
    Digitale Medien
    Digitale Medien
    A space decomposition method for parabolic equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 27-46 
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    ISSN: 0749-159X
    Schlagwort(e): Parallel ; domain decomposition ; parabolic equation ; space decomposition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A convergence proof is given for an abstract parabolic equation using general space decomposition techniques. The space decomposition technique may be a domain decomposition method, a multilevel method, or a multigrid method. It is shown that if the Euler or Crank-Nicolson scheme is used for the parabolic equation, then by suitably choosing the space decomposition, only O(| log τ |) steps of iteration at each time level are needed, where τ is the time-step size. Applications to overlapping domain decomposition and to a two-level method are given for a second-order parabolic equation. The analysis shows that only a one-element overlap is needed. Discussions about iterative and noniterative methods for parabolic equations are presented. A method that combines the two approaches and utilizes some of the good properties of the two approaches is tested numerically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 27-46, 1998
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  • 23
    Digitale Medien
    Digitale Medien
    Preconditioners for the p-version of the Galerkin method for a coupled finite element/boundary element system (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 47-61 
    Details
    ISSN: 0749-159X
    Schlagwort(e): p-version finite element method ; boundary element method ; interface problem ; preconditioning ; domain decomposition ; additive Schwarz method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We propose and analyze efficient preconditioners for solving systems of equations arising from the p-version for the finite element/boundary element coupling. The first preconditioner amounts to a block Jacobi method, whereas the second one is partly given by diagonal scaling. We use the generalized minimum residual method for the solution of the linear system. For our first preconditioner, the number of iterations of the GMRES necessary to obtain a given accuracy grows like log2 p, where p is the polynomial degree of the ansatz functions. The second preconditioner, which is more easily implemented, leads to a number of iterations that behave like p log3 p. Computational results are presented to support this theory. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 47-61, 1998
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  • 24
    Digitale Medien
    Digitale Medien
    Gauss point mass lumping schemes for Maxwell's equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 63-88 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Maxwell equations ; edge finite elements ; mass lumping ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite element and finite difference methods for approximating the Maxwell system propagate numerical waves with slightly incorrect velocities, and this results in phase error in the computed solution. Indeed this error limits the type of problem that can be solved, because phase error accumulates during the computation and eventually destroys the solution. Here we propose a family of mass-lumped finite element schemes using edge elements. We emphasize in particular linear elements that are equivalent to the standard Yee FDTD scheme, and cubic elements that have superior phase accuracy. We prove theorems that allow us to perform a dispersion analysis of the two common families of edge elements on rectilinear grids. A result of this analysis is to provide some justification for the choice of the particular family we use. We also provide a limited selection of numerical results that show the efficiency of our scheme. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 63-88, 1998
    Zusätzliches Material: 4 Ill.
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  • 25
    Digitale Medien
    Digitale Medien
    Superconvergent recovery of gradients of piecewise linear finite element approximations on non-uniform mesh partitions (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 169-192 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element space ; (1 + α˜)-regular mesh partition ; recovered gradient ; superconvergence ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We propose the use of an averaging scheme, which recovers gradients from piecewise linear finite element approximations on the (1 + α˜) - regular triangular elements to gradients of the weak solution of a second-order elliptic boundary value problem in the 2-dimensional space. The recovered gradients, from mid-points of element edges, are superconvergent estimates of the true gradients. This work is an extension of Levine [Levine, IMA J. Numer. Anal. 5, 407 (1985)] and follows some of the ideas therein. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:169-192, 1998
    Zusätzliches Material: 10 Ill.
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  • 26
    Digitale Medien
    Digitale Medien
    Finite volume methods on Voronoi meshes (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 193-212 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Cell-centered finite differences ; upwind approximations ; error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Two cell-centered finite difference schemes on Voronoi meshes are derived and investigated. Stability and error estimates in a discrete H1-norm for both symmetric and nonsymmetric problems, including convection dominated, are proven. The theoretical results are illustrated with several numerical experiments. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:193-212, 1998
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  • 27
    Digitale Medien
    Digitale Medien
    Convergence analysis of a finite volume method via a new nonconforming finite element method (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 213-231 
    Details
    ISSN: 0749-159X
    Schlagwort(e): cell-centered finite volume method ; convergence ; finite element method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The article is devoted to the study of convergence properties of a Finite Volume Method (FVM) using Voronoi boxes for discretization. The approach is based on the construction of a new nonconforming Finite Element Method (FEM), such that the system of linear equations coincides completely with that for the FVM. Thus, by proving convergence properties of the FEM, we obtain similar ones of the FVM. In this article, the investigations are restricted to the Poisson equation. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:213-231, 1998
    Zusätzliches Material: 2 Ill.
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  • 28
    Digitale Medien
    Digitale Medien
    A numerical method for problems in infinite strips with irregularities extending to infinity (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 233-249 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Infinite domain ; semi-infinite strip ; Dirichlet-to-Neumann ; Finite element ; variable coefficients ; nonlinear elliptic PDEs ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirichlet-to-Neumann (DtN) Finite Element Method is a combined analytic-numerical method for boundary value problems in infinite domains. The use of this method is usually based on the assumption that, in the infinite domain D exterior to the finite computational domain, the governing differential equations are sufficiently simple. In particular, in D it is generally assumed that the equations are linear, homogeneous, and have constant coefficients. In this article, an extension of the DtN method is proposed, which can be applied to elliptic problems with “irregularities” in the exterior domain D, such as (a) inhomogeneities, (b) variable coefficients, and (c) nonlinearities. This method is based on iterative “regularization” of the problem in D, and on the efficient treatment of infinite-domain integrals. Semi-infinite strip problems are used for illustrating the method. Convergence of the iterative process is analyzed both theoretically and numerically. Nonuniformity difficulties and a way to overcome them are discussed. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:233-249, 1998
    Zusätzliches Material: 7 Ill.
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  • 29
    Digitale Medien
    Digitale Medien
    Moving finite element methods by use of space-time elements: I. Scalar problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 251-262 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Moving finite element ; discontinuous Galerkin ; space-time orientation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article deals with moving finite element methods by use of the time-discontinuous Galerkin formulation in combination with oriented space-time meshes. A principle for mesh orientation in space-time based on minimization of the residual, related to adaptive error control via an a posteriori error estimate, is presented. The relation to Miller's moving finite element method is discussed. The article deals with scalar problems; systems will be treated in a companion article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:251-262, 1998
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  • 30
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    Digitale Medien
    On convergence and performance of iterative methods with fourth-order compact schemes (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 263-280 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Convection-diffusion equation ; iterative methods ; fourth-order compact discretization schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the convergence and performance of iterative methods with the fourth-order compact discretization schemes for the one- and two-dimensional convection-diffusion equations. For the one-dimensional problem, we investigate the symmetrizability of the coefficient matrix and derive an analytical formula for the spectral radius of the point Jacobi iteration matrix. For the two-dimensional problem, we conduct Fourier analysis to determine the error reduction factors of several basic iterative methods and comment on their potential use as the smoothers for the multilevel methods. Finally, we perform numerical experiments to verify our Fourier analysis results. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:263-280, 1998
    Zusätzliches Material: 10 Ill.
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  • 31
    Digitale Medien
    Digitale Medien
    An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 281-296 
    Details
    ISSN: 0749-159X
    Schlagwort(e): singularities ; elliptic PDE ; Laplace equation ; high-order Finite Difference Schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicinity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is “pollution” free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson equations over domains containing re-entrant corners or abrupt changes in the boundary conditions are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 281-296, 1998
    Zusätzliches Material: 9 Ill.
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  • 32
    Digitale Medien
    Digitale Medien
    Qualitative behavior of numerical solutions to an s-i-s epidemic model (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 317-337 
    Details
    ISSN: 0749-159X
    Schlagwort(e): s-i-s epidemic model ; finite difference ; method of characteristics ; asymptotic behavior ; periodic solution ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A finite difference scheme along the characteristics is used to approximate the solution of an age-dependent s-i-s epidemic model. The global behavior of the discrete solution resulting from the algorithm is investigated. It is shown that a nontrivial discrete periodic solution is generated by a periodic force of infection. Sufficient (and explicit) threshold conditions for the existence and stability of a unique nontrivial periodic solution are given. Results from numerical experiments are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 317-337, 1998
    Zusätzliches Material: 8 Ill.
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  • 33
    Digitale Medien
    Digitale Medien
    Mesh-centered finite differences from nodal finite elements for elliptic problems (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 439-465 
    Details
    ISSN: 0749-159X
    Schlagwort(e): mesh-centered finite differences ; nodal methods ; elliptic problems ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: After it is shown that the classical five-point mesh-centered finite difference scheme can be derived from a low-order nodal finite element scheme by using nonstandard quadrature formulae, higher-order block mesh-centered finite difference schemes for second-order elliptic problems are derived from higher-order nodal finite elements with nonstandard quadrature formulae as before, combined to a procedure known as “transverse integration.” Numerical experiments with uniform and nonuniform meshes and different types of boundary conditions confirm the theoretical predictions, in discrete as well as continuous norms. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 439-465, 1998
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  • 34
    Digitale Medien
    Digitale Medien
    Nonstandard methods for the convective transport equation with nonlinear reactions (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 467-485 
    Details
    ISSN: 0749-159X
    Schlagwort(e): convection-reaction equations ; Lagrangian methods ; convective flows ; reactive solute transport problems ; exact finite difference schemes ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467-485, 1998
    Zusätzliches Material: 6 Ill.
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  • 35
    Digitale Medien
    Digitale Medien
    A posteriori error estimates for nonlinear problems: Lr, (0, T; W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 487-518 
    Details
    ISSN: 0749-159X
    Schlagwort(e): A posteriori error estimates ; nonlinear parabolic PDEs ; time-dependent Navier-Stokes equations ; space-time finite elements ; θ-scheme ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Using the abstract framework of [R. Verfürth, Math. Comput. 62, 445-475 (1996)], we analyze a residual a posteriori error estimator for space-time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicolson scheme. As particular examples we consider scalar quasilinear parabolic PDEs of 2nd order and the time-dependent incompressible Navier-Stokes equations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 487-518, 1998
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    Digitale Medien
    Digitale Medien
    A note on Hermitian splitting induced relaxation methods for convection-diffusion equations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 581-591 
    Details
    ISSN: 0749-159X
    Schlagwort(e): iterative methods ; Hermitian splitting ; successive overrelaxation ; convection-diffusion equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The solution of the linear system Ax = b by iterative methods requires a splitting of the coefficient matrix in the form A = M - N where M is usually chosen to be a diagonal or a triangular matrix. In this article we study relaxation methods induced by the Hermitian and skew-Hermitian splittings for the solution of the linear system arising from a compact fourth order approximation to the one dimensional convection-diffusion equation and compare the convergence rates of these relaxation methods to that of the widely used successive overrelaxation (SOR) method. Optimal convergence parameters are derived for each method and numerical experiments are given to supplement the theoretical estimates. For certain values of the diffusion parameter, a relaxation method based on the Hermitian splitting converges faster than SOR. For two-dimensional problems a block form of the iterative algorithm is presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 581-591, 1998
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  • 37
    Digitale Medien
    Digitale Medien
    Discretization of the stationary convection-diffusion-reaction equation (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 607-625 
    Details
    ISSN: 0749-159X
    Schlagwort(e): convection-diffusion-reaction equation ; finite volume method ; exponential scheme ; flux computation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A finite volume method for the convection-diffusion-reaction equation is presented, which is a model equation in combustion theory. This method is combined with an exponential scheme for the computation of the fluxes. We prove that the numerical fluxes are second-order accurate, uniformly in the local Peclet numbers. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 607-625, 1998
    Zusätzliches Material: 4 Ill.
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  • 38
    Digitale Medien
    Digitale Medien
    Dimensional splitting with front tracking and adaptive grid refinement (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 627-648 
    Details
    ISSN: 0749-159X
    Schlagwort(e): scalar conservation laws ; dimensional splitting ; front tracking ; error bounds ; adaptive grid refinement ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Front tracking in combination with dimensional splitting is analyzed as a numerical method for scalar conservation laws in two space dimensions. An analytic error bound is derived, and convergence rates based on numerical experiments are presented. Numerical experiments indicate that large CFL numbers can be used without loss of accuracy for a wide range of problems. A new method for grid refinement is introduced. The method easily allows for dynamical changes in the grid, using, for instance, the total variation in each grid cell as a criterion for introducing new or removing existing refinements. Several numerical examples are included, highlighting the features of the numerical method. A comparison with a high-resolution method confirms that dimensional splitting with front tracking is a highly viable numerical method for practical computations. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 627-648, 1998
    Zusätzliches Material: 11 Ill.
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  • 39
    Digitale Medien
    Digitale Medien
    On the linear stability study of zonal incompressible flows on a sphere (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 649-665 
    Details
    ISSN: 0749-159X
    Schlagwort(e): linear stability ; zonal flows ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The normal mode (linear) stability of zonal flows of a nondivergent fluid on a rotating sphere is considered. The spherical harmonics are used as the basic functions on the sphere. The stability matrix representing in this basis the vorticity equation operator linearized about a zonal flow is analyzed in detail using the recurrent formula derived for the nonlinear triad interaction coefficients. It is shown that the zonal flow having the form of a Legendre polynomial Pn(μ) of degree n is stable to infinitesimal perturbations of every invariant set Im with |m| ≥ n. For each zonal number m, Im is here the span of all the spherical harmonics $Y^{m}_{k}(x)$, whose degree k is greater than or equal to m. It is also shown that such small-scale perturbations are stable not only exponentially, but also algebraically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 649-665, 1998
    Zusätzliches Material: 4 Ill.
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  • 40
    Digitale Medien
    Digitale Medien
    Least squares methods for Volterra equations and generalizations (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 679-693 
    Details
    ISSN: 0749-159X
    Schlagwort(e): least squares method ; finite element method ; Volterra equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679-693, 1998
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.10501
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    Digitale Medien
    The Method of Fundamental Solutions for Stokes flows with a free surface (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 667-678 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Method of fundamental solutions ; elliptic boundary value problems ; Stokes flow ; free surface ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We investigate the use of the Method of Fundamental Solutions (MFS) for solving Stokes flow problems with a free surface. We apply the method to the creeping planar Newtonian extrudate-swell problem and study the effect of the surface tension on the free surface. The results are in good agreement with existing finite element and boundary element solutions. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 667-678, 1998
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.10500
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  • 42
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    Digitale Medien
    A family of ELLAM schemes for advection-diffusion-reaction equations and their convergence analyses (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 14 (1998), S. 739-780 
    Details
    ISSN: 0749-159X
    Schlagwort(e): advection-diffusion-reaction transport equations ; characteristic methods ; error estimates ; Eulerian-Lagrangian methods ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A family of ELLAM (Eulerian-Lagrangian localized adjoint method) schemes is developed and analyzed for linear advection-diffusion-reaction transport partial differential equations with any combination of inflow and outflow Dirichlet, Neumann, or flux boundary conditions. The formulation uses space-time finite elements, with edges oriented along Lagrangian flow paths, in a time-stepping procedure, where space-time test functions are chosen to satisfy a local adjoint condition. This allows Eulerian-Lagrangian concepts to be applied in a systematic mass-conservative manner, yielding numerical schemes defined at each discrete time level. Optimal-order error estimates and superconvergence results are derived. Numerical experiments are performed to verify the theoretical estimates. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 739-780, 1998
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  • 43
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    Digitale Medien
    Error estimates using the cell discretization method for second-order hyperbolic equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 531-548 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Hyperbolic second-order partial differential equations ; nonconforming finite element methods ; primal hybrid method ; cell discretization ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The cell discretization algorithm provides approximate solutions to second-order hyperbolic equations with coefficients independent of time. We obtain error estimates that show general convergence for homogeneous problems using semi-discrete approximations. A polynomial implementation of the algorithm is described that is a nonconforming extension of the finite element method that can also produce the continuous approximations of an h-p finite element method. Numerical tests are made that confirm the theoretical estimates. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 531-548, 1997
    Zusätzliches Material: 3 Ill.
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  • 44
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    Digitale Medien
    Analysis of finite element approximation and quadrature of Volterra integral equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 663-672 
    Details
    ISSN: 0749-159X
    Schlagwort(e): finite element method ; Volterra integral equations ; Galerkin method ; projection method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article we study Galerkin finite element approximations to integral equations of the Volterra type. Our prime concern is the noncoercive case, which is not covered by the standard finite element theory. The question of rates of convergence is studied for the case where an exact stiffness matrix is available, as well as the case where the latter is approximated via quadrature rules. The optimality of these rules is also considered from the point of view of the effect the choice of the quadrature has on the overall rate of convergence. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 663-672, 1997
    Zusätzliches Material: 5 Ill.
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  • 45
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    Digitale Medien
    Runge-Kutta characteristic methods for first-order linear hyperbolic equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 617-661 
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    ISSN: 0749-159X
    Schlagwort(e): characteristic methods ; Eulerian-Langrangian methods ; numerical solution of first-order hyperbolic equations ; Runge-Kutta methods ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We develop two Runge-Kutta characteristic methods for the solution of the initial-boundary value problems for first-order linear hyperbolic equations. One of the methods is based on a backtracking of the characteristics, while the other is based on forward tracking. The derived schemes naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary condition. They are fully mass conservative and can be viewed as higher-order time integration schemes improved over the ELLAM (Eulerian-Lagrangian localized adjoint method) method developed previously. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices. Extensive numerical results are presented to compare the performance of these methods with many well studied and widely used methods, including the Petrov-Galerkin methods, the streamline diffusion methods, the continuous and discontinuous Galerkin methods, the MUSCL, and the ENO schemes. The numerical experiments also verify the optimal-order convergence rates of the Runge-Kutta methods developed in this article. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 617-661, 1997
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    Digitale Medien
    Digitale Medien
    Parallel block iterative method for multiaquifer flow models (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 39-50 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Flow in a multiaquifer porous system can be simulated by the so-called “quasi three-dimensional” models. When heterogeneous and/or aquitards with nonlinear hydrogeologic behavior are considered, a fully numerical approach is required for the model solution. If the finite element method is used to integrate the partial differential flow equations, the final solution of large systems is required. In the present article, an original iterative solution strategy is developed. The global system is decoupled into a number of smaller subsystems consistent with the geologic structure (aquitards and aquifers) of the multiaquifer system. The aquifer and the aquitard equations are solved separately with the modified conjugate gradient and the Thomas algorithms, respectively, while the final coupled solution is obtained with an iterative procedure equivalent to a Block Jacobi scheme. The procedure can be efficiently implemented on a parallel super-computer distributing the computational load, so that two successive blocks (related to an aquifer and the underlying aquitard) are solved on the same processor. The procedure is analyzed with linear porous media, where the convergence is theoretically ensured. The results obtained with a realistic linear multiaquifer system, employing a massively parallel computer like the CRAY T3D, have pointed out the high degree of parallelization of the algorithm. Comparison with the parallel implementation of the Block SOR and Block Gauss-Seidel schemes shows that parallel Block Jacobi performs significantly better with a reduction of the elapsed times, which depends on the rate of leakage between neighboring aquifers. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    Relation between the time and space step-sizes in nonstandard finite-difference schemes for the Fisher equation (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 51-55 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A positivity condition is used to obtain functional relations between the time and space step-sizes for nonstandard finite-difference models of the Fisher partial differential equation. An upper bound is also derived for the solutions to the difference equations. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    Accelerated multigrid high accuracy solution of the convection-diffusion equation with high Reynolds number (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 77-92 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A fourth-order compact finite difference scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diffusion equation with very high Reynolds number and variable coefficients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver is stable and yields accurate solution for high Reynolds number problems. We also show that the MRS acceleration procedure is efficient and the acceleration cost is negligible. © 1997 John Wiley & Sons, Inc.
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    The study on the nonlinear computations of the DQ and DC methods (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 57-75 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article points out that the differential quadrature (DQ) and differential cubature (DC) methods, due to their global domain property, are more efficient for nonlinear problems than the traditional numerical techniques such as finite element and finite difference methods. By introducing the Hadamard product of matrices, we obtain an explicit matrix formulation for the DQ and DC solutions of nonlinear differential and integro-differential equations. Due to its simplicity and flexibility, the present Hadamard product approach makes the DQ and DC methods much easier to use. Many studies on the Hadamard product can be fully exploited for the DQ and DC nonlinear computations. Furthermore, we first present the SJT product of matrix and vector to compute accurately and efficiently the Frechet derivative matrix in the Newton-Raphson method for the solution of the nonlinear formulations. We also propose a simple approach to simplify the DQ or DC formulations for some nonlinear differential operators and, thus, the computational efficiency of these methods is significantly improved. We give the matrix multiplication formulas to efficiently compute the weighting coefficient matrices of the DC method. The spherical harmonies are suggested as the test functions in the DC method to handle the nonlinear differential equations occurring in global and hemispheric weather forecasting problems. Some examples are analyzed to demonstrate the simplicity and efficiency of the presented techniques. It is emphasized that the innovations presented are applicable to the nonlinear computations of the other numerical methods as well. © 1997 John Wiley & Sons, Inc.
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    A residual-based a posteriori error estimator for the Ciarlet-Raviart formulation of the first biharmonic problem (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 93-111 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article we propose a residual-based estimator for the psi-omega formulation of the biharmonic problem. We show how an appropriate modification of Verfürth methodology gives the proper scaling of the residuals leading to both lower and upper estimation. Numerical examples confirm the viability of the method. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    An improved coarse-mesh nodal integral method for partial differential equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 113-145 
    Details
    ISSN: 0749-159X
    Schlagwort(e): coarse-mesh ; nonlinear PDEs ; Burgers equation ; inherent upwinding ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An improved variation of the nodal integral method to solve partial differential equations has been developed and implemented. Rather than treating all of the nonlinear terms as the so-called pseudo-source terms (to be approximated), in this modified version of the nodal integral method, by approximating part of the nonlinear terms in terms of the discrete variable(s) that ultimately result at the end of the formulation process, some or all of the nonlinear terms are kept on the left-hand side in the transverse-integrated equations, which are to be solved analytically. Application of the method to solve the Burgers equation leads to exponential variation within the nodes and shows that the resulting scheme has inherent upwinding. Reconstruction of node interior solution - as a function of one independent variable, and averaged in all others - makes it possible to obtain rather accurate solutions even on a fine scale. Results of the numerical analysis and comparison with results of other methods reported in the literature show that the new method is comparable and sometimes better in accuracy than the currently used schemes. Extension to multidimensional, time-dependent problems is straightforward. © 1997 John Wiley & Sons, Inc.
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    Analysis and convergence of a MAC-like scheme for the generalized Stokes problem (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 147-162 
    Details
    ISSN: 0749-159X
    Schlagwort(e): covolume methods ; MAC schemes ; mixed methods ; Stokes problem ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We introduce a MAC-like scheme (a covolume method on rectangular grids) for approximating the generalized Stokes problem on an axiparallel domain. Two staggered grids are used in the derivation of the discretization. The velocity is approximated by conforming bilinears over rectangular elements, and the pressure by piecewise constants over macro-rectangular elements. The error in the velocity in the H1 norm and the pressure in the L2 norm are shown to be of first order, provided that the exact velocity is in H2 and the exact pressure in H1, and that the partition family of the domain is regular. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    A least-square mixed method for Stokes equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 191-199 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove the convergence of a least-square mixed method for Stokes equations by use of an operator theoretic approach. The method does not require LBB condition on the finite dimensional subspaces. The resulting bilinear form is symmetric and positive definite, which leads to optimal convergence and the h-2 condition number. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    On the convergence of a combined finite volume-finite element method for nonlinear convection-diffusion problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 163-190 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume mesh dual to a triangular grid, whereas the diffusion term is discretized by piecewise linear conforming triangular elements. Under the assumption that the triangulations are of weakly acute type, with the aid of the discrete maximum principle, a priori estimates, and some compactness arguments based on the use of the Fourier transform with respect to time, the convergence of the approximate solutions to the exact solution is proved, provided that the mesh size tends to zero. © 1997 John Wiley & Sons, Inc.
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    How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 201-214 
    Details
    ISSN: 0749-159X
    Schlagwort(e): tetrahedral meshes ; local refinements ; finite elements ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A simple algorithm that generates local refinements of tetrahedral meshes is proposed. Refinements are made by tetrahedra, which are subdivided into eight, four, three, or two smaller tetrahedra. We prove that a regularity ball condition is satisfied for the refined mesh. This guarantees that tetrahedra do not become flat when the mesh size tends to zero. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    Numerical solution of the generalized Stokes problem for the flow in a channel (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 237-256 
    Details
    ISSN: 0749-159X
    Schlagwort(e): flow in a channel ; separation of variables ; incremental unknowns ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article we introduce the separation of variables in the two-dimensional generalized Stokes problem. -νΔu + αu + inverted delta p = f, for the flow in a channel. Also for the first time, we discuss the implementation of the Incremental Unknowns Method with a data structure of Compressed Column Storage. Two examples of application of the Incremental Unknowns method for this problem are presented in which we compare the CPU times of three methods: Conjugate Gradient (CG), Incremental Unknowns (IU), and Uzawa Algorithm (Uzawa). © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    Mixed finite volume methods for semiconductor device simulation (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 215-236 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We deal with the two-dimensional numerical solution of the Van Roosbroeck system, widely employed in modern semiconductor device simulation. Using the well-known Gummel's decoupled algorithm leads to the iterative solution of a nonlinear Poisson equation for the electric potential and two linearized continuity equations for the electron and hole current densities. The numerical approximation is based on the dual mixed formulation for a self-adjoint second-order elliptic operator by using the Raviart-Thomas (RT) finite elements of lowest degree on a triangular partition of the device domain. In this article, we propose a suitable variant of the RT method, based on the diagonalization of the element mass matrix. This is achieved by use of an appropriate numerical integration that eliminates the fluxes and gives rise to a cell-centered finite volume scheme for the scalar unknown with the same approximation properties of the mixed approach, but at a reduced computational cost. The above procedure suggests also a natural way to introduce in the frame of the classical Box Method (BM) suitable vector basis functions (edge elements) to represent the current field over each mesh triangle. This issue may be profitably employed both as a postprocessing tool, as well as a technique for solving the current continuity equations when source terms depending on the current itself are included in the mathematical model. Simulations of realistic semiconductor devices are then included to demonstrate the accuracy and stability of the new method. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    A frequency accurate spatial derivative finite difference approximation (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 549-560 
    Details
    ISSN: 0749-159X
    Schlagwort(e): frequency accurate methods ; finite difference approximations ; fourier transforms ; partial differential equations ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present a method for designing spatial derivative approximations that achieves a priori accuracy in the spatial frequency domain. We use a general, average value approximation with undetermined coefficients together with a set of constraints that ensure convergence and consistency to formulate a constrained optimal fitting problem. These constraints lead to a linear matrix formulation. We apply the method to the design of spatial approximations for simulating equations with wavelike solutions using both an explicit central difference approximation (which has no phase error) and an upwind design where the level of dissipation can be specified by the designer. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 549-560, 1997
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    Digitale Medien
    On the Eulerian-Lagrangian formulation of balance equations in porous media (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 505-530 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Porous medium ; modeling ; transport phenomena ; Eulerian-Lagrangian formulation ; primary variables ; reduced velocities ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The article presents a general approach to modeling the transport of extensive quantities in the case of flow of multiple multicomponent fluid phases in a deformable porous medium domain under nonisothermal conditions. The models are written in a modified Eulerian-Lagrangian formulation. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. The advantage of this formulation, with respect to the usually employed Eulerian one, is that numerical dispersion, associated with the advective fluxes of extensive quantities, are eliminated. The methodology presented in the article shows how the Eulerian-Lagrangian formulation is written in terms of the relatively small number of primary variables of a transport problem. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 505-530, 1997
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    Digitale Medien
    Front tracking for two-phase flow in reservoir simulation by adaptive mesh (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 673-697 
    Details
    ISSN: 0749-159X
    Schlagwort(e): porous media ; adaptive mesh ; MUSCL scheme ; OOP ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, an algorithm for the numerical approximation of two-phase flow in porous media by adaptive mesh is presented. A convergent and conservative finite volume scheme for an elliptic equation is proposed, together with the finite difference schemes, upwind and MUSCL, for a hyperbolic equation on grids with local refinement. Hence, an IMPES method is applied in an adaptive composite grid to track the front of a moving solution. An object-oriented programmation technique is used. The computational results for different examples illustrate the efficiency of the proposed algorithm. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 673-697, 1997
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    A parallel spectral Fourier-Nonlinear Galerkin algorithm for simulation of turbulence (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 699-715 
    Details
    ISSN: 0749-159X
    Schlagwort(e): parallel algorithm ; domain decomposition ; Local Fourier Basis ; Nonlinear Galerkin Method ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present a high-order parallel algorithm, which requires only the minimum interprocessor communication dictated by the physical nature of the problem at hand. The parallelization is achieved by domain decomposition. The discretization in space is performed using the Local Fourier Basis method. The continuity conditions on the interfaces are enforced by adding homogeneous solutions. Such solutions often have fast decay properties, which can be utilized to minimize interprocessor communication. In effect, the predominant part of the computation is performed independently in the subdomains (processors) or using only local communication. A novel element of the present parallel algorithm is the incorporation of a Nonlinear Galerkin strategy to accelerate the computation and stabilize the time integration process. The basic idea of this approach consists of decomposition of the variables into large scale and small scale components with different treatment of these large and small scales. The combination of the Multidomain Fourier techniques with the Nonlinear Galerkin (NLG) algorithm is applied here to solve incompressible Navier-Stokes equations. Results are presented on direct numerical simulation of two-dimensional homogeneous turbulence using the NLG method. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 699-715, 1997
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    Analysis of strain-pressure finite element methods for the Stokes problem (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 717-730 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Stokes ; enhanced strains ; inf-sup condition ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An analysis of some nonconforming approximations of the Stokes problem is presented. The approximations are based on a strain-pressure variational formulation. In particular, a convergence and stability result for a method recently proposed by Bathe and Pantuso is provided. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 717-730, 1997
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    Digitale Medien
    A consistent approach to variable bubble-point systems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 1-18 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Here, it is shown that the “traditional approach” to variable bubble-point problems, using black-oil models, is not consistent, because it violates the “bubble-point conservation law.” In order to have a consistent approach, it is necessary to incorporate shocks - discussed in previous papers - in which the bubble-point is discontinuous. A “consistent approach” is applied to specific examples, and results compared with those of the “traditional” one. The conclusion that the “traditional approach” generally yields large errors for the production rates and other parameters of interest in the oil industry, is reached. © 1997 John Wiley & Sons, Inc.
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    Vorticity-velocity formulation for the Navier-Stokes equations: The three-dimensional case (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 19-38 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we propose a mixed method for the vorticity-velocity formulation of the stationary Stokes and Navier-Stokes equations in space dimension three, the unknowns being the vorticity and the velocity of the fluid. We give a similar variational formulation for the nonstationary Stokes equations in the vorticity-velocity variables. © 1997 John Wiley & Sons, Inc.
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    An iterative penalty method for the least squares solution of boundary value problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 257-281 
    Details
    ISSN: 0749-159X
    Schlagwort(e): boundary value problems ; collocation least squares method ; augmented Lagrangian method ; Uzawa's algorithm ; preconditioned conjugate gradient ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article is concerned with iterative techniques for linear systems of equations arising from a least squares formulation of boundary value problems. In its classical form, the solution of the least squares method is obtained by solving the traditional normal equation. However, for nonsmooth boundary conditions or in the case of refinement at a selected set of interior points, the matrix associated with the normal equation tends to be ill-conditioned. In this case, the least squares method may be formulated as a Powell multiplier method and the equations solved iteratively. Therein we use and compare two different iterative algorithms. The first algorithm is the preconditioned conjugate gradient method applied to the normal equation, while the second is a new algorithm based on the Powell method and formulated on the stabilized dual problem. The two algorithms are first compared on a one-dimensional problem with poorly conditioned matrices. Results show that, for such problems, the new algorithm gives more accurate results. The new algorithm is then applied to a two-dimensional steady state diffusion problem and a boundary layer problem. A comparison between the least squares method of Bramble and Schatz and the new algorithm demonstrates the ability of the new method to give highly accurate results on the boundary, or at a set of given interior collocation points without the deterioration of the condition number of the matrix. Conditions for convergence of the proposed algorithm are discussed. © 1997 John Wiley & Sons, Inc.
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    Coiflet interpolation and approximate solutions of elliptic partial differential equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 303-320 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we prove a higher order interpolation result for square-integrable functions by using generalized coiflets. Convergence of approximation by using generalized coiflets is shown. Applications to wavelet-Galerkin approximation of elliptic partial differential equations and some numerical examples are also given. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13:303-320, 1997.
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    A preconditioning strategy for boundary element Galerkin methods (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 283-301 
    Details
    ISSN: 0749-159X
    Schlagwort(e): boundary element method ; preconditioner ; conjugate gradient method ; mesh grading ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirichlet and Neumann problems for the Laplacian are reformulated in the usual way as boundary integral equations of the first kind with symmetric kernels. These integral equations are solved using Galerkin's method with piecewise-constant and piecewise-linear boundary elements, respectively. In both cases, the stiffness matrix is symmetric and positive-definite, and has a condition number of order N, the number of degrees of freedom. By contrast, the condition number of the product of the two stiffness matrices is bounded independently of N. Hence, we can use the Neumann stiffness matrix to precondition the Dirichlet stiffness matrix, and vice versa. © 1997 John Wiley & Sons, Inc.
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    Digitale Medien
    On preconditioned Krylov subspace methods for discrete convection-diffusion problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 321-330 
    Details
    ISSN: 0749-159X
    Schlagwort(e): convection-diffusion equation ; preconditioners ; Krylov subspace methods ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study nonstationary iterative methods for solving preconditioned systems arising from discretizations of the convection-diffusion equation. The preconditioners arise from Gauss-Seidel methods applied to the original system. It is shown that the performance of the iterative solvers is affected by the relationship of the ordering of the underlying grid and the direction of the fow associated with the differential operator. Specifically, only those orderings that follow the fow give fast iterative solvers. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13:321-330
    Zusätzliches Material: 7 Ill.
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  • 69
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    Digitale Medien
    A Gauss-Galerkin finite-difference method for singular partial differential equations in two space variables (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 331-355 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Gauss-Galerkin ; finite-difference ; semi-discrete difference approximation ; weak convergence ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A Gauss-Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss-Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are presented. These numerical results are encouraging and suggest that the proposed method is efficient in treating singular parabolic partial differential equations of the type considered here. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 331-355, 1997
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    A family of fourth-order parallel splitting methods for parabolic partial differential equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 357-373 
    Details
    ISSN: 0749-159X
    Schlagwort(e): heat equation ; finite differences ; parallel splitting ; fourth-order numerical methods ; avoiding complex arithmetic ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A family of numerical methods which are L-stable, fourth-order accurate in space and time, and do not require the use of complex arithmetic is developed for solving second-order linear parabolic partial differential equations. In these methods, second-order spatial dderivatives are approximated by fourth-order finite-difference approximations, and the matrix exponential function is approximated by a rational approximation consisting of three parameters. Parallel algorithms are developed and tested on the one-dimensional head equation, with constant coefficients, subject to homogeneous and time-dependent boundary conditions. These methods are also extended to two- and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 357-373, 1997
    Zusätzliches Material: 8 Tab.
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  • 71
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    Galerkin method for a Stefan-type problem in one space dimension (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 393-416 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Galerkin method ; Stefan problem ; fixed domain method ; optimal error estimates ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Based on a Landau-type transformation, both continuous and discrete in time L2-Galerkin methods are applied to a single-phase Stefan-type problem in one space dimension. Optimal rates of convergence in Lℵ, L∞, and H1-norms are derived and computational results are presented. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 393-416, 1997
    Zusätzliches Material: 6 Ill.
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  • 72
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    A highly accurate numerical solution of a biharmonic equation (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 375-391 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Biharmonic equation ; finite difference ; high-order accuracy ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The coefficients for a nine-point high-order accuracy discretization scheme for a biharmonic equation ∇ 4u = f(x, y) (∇2 is the two-dimensional Laplacian operator) are derived. The biharmonic problem is defined on a rectangular domain with two types of boundary conditions: (1) u and ∂2u/∂n2 or (2) u and ∂u/part;n (where ∂/part;n is the normal to the boundary derivative) are specified at the boundary. For both considered cases, the truncation error for the suggested scheme is of the sixth-order O(h6) on a square mesh (hx = hy = h) and of the fourth-order O(h4xh2xh2y h4y) on an unequally spaced mesh. The biharmonic equation describes the deflection of loaded plates. The advantage of the suggested scheme is demonstrated for solving problems of the deflection of rectangular plates for cases of different boundary conditions: (1) a simply supported plate and (2) a plate with built-in edges. In order to demonstrate the high-order accuracy of the method, the numerical results are compared with exact solutions. © John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 375-391, 1997
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  • 73
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    A legendre pseudospectral method for a PDE model for the dynamics of infectious diseases (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 417-432 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Legendre pseudospectral method ; infectious diseases ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A Legendre pseudospectral method is developed for a PDE model for the dynamics of infectious diseases. The stability and the convergence rate of the method are studied. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 417-432, 1997
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  • 74
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    Convergence analysis of a staggered pressure correction scheme for viscous incompressible flows (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 459-482 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Convergence analysis ; pressure correction scheme ; viscous incompressible flows ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article performs the convergence analysis of a staggered pressure correction scheme for solving unsteady viscous incompressible flows in a bounded domain using the energy method. Error estimates for the numerical velocity field of the difference scheme are established. The analysis adopts the method of bounded truncation functions as advocated by Arnold et al. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 459-482, 1997
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    On the convergence of a certain type of nonlinear lumped energy equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 433-443 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Recently, Campo and Lacoa [Campo & Lacoa, Numerical Methods Partial Differential Eq., 11, 275 (1995)] proposed a simple iterative procedure to solve approximately a forced convection heat-transfer problem inside a tube subjected to nonlinear convective boundary conditions. Their technique relied on solutions of a one-dimensional ordinary differential equation of first order to estimate the behavior of the solution of the two-dimensional parabolic partial differential equation. The recursive steps, proposed by Campo and Lacoa, can be combined in a single fixed-point iteration formula thus facilitating the study of its properties. In this note, we present a short analysis of the convergence of the Campo-Lacoa equation and give alternatives to guarantee and improve the convergence patterns. Our results show that the Picard's iterative method converges for all values of Z in the region of thermal development, e.g., 0 ≤ Z ≤ 1; however, the convergence rate tends to diminish as Z increases. To guarantee convergence for larger values of Z, a damped-Picard's iteration may be adopted. Moreover, to increase the rate of convergence, a Newton's iteration is proposed. A detailed comparison in terms of accuracy and CPU time is provided. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 433-443, 1997
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    Digitale Medien
    A nonconforming mixed finite element for second-order elliptic problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 445-457 
    Details
    ISSN: 0749-159X
    Schlagwort(e): nonconforming mixed finite elements ; nonconforming piecewise quadratic approximations ; second-order elliptic problems ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to construct a nonconforming mixed finite element for the lowest order case. We prove the convergence and give estimates of optimal order for this finite element. Our proof is based on the use of the properties of the so-called nonconforming bubble function to control the consistency terms introduced by the nonconforming approximation. We further establish an equivalence between this mixed finite element and the nonconforming piecewise quadratic finite element of Fortin and Soulie [J. Numer. Methods Eng., 19, 505-520, 1983]. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 445-457, 1997
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    Analysis of expanded mixed methods for fourth-order elliptic problems (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 483-503 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Expanded mixed methods ; finite elements ; error estimates ; fourth-order elliptic problems ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The recently proposed expanded mixed formulation for numerical solution of second-order elliptic problems is here extended to fourth-order elliptic problems. This expanded formulation for the differential problems under consideration differs from the classical formulation in that three variables are treated, i.e., the displacement, the stress, and the moment tensors. It works for the case where the coefficient of the differential equations is small and does not need to be inverted, or for the case in which the stress tensor of the equations does not need to be symmetric. Based on this new formulation, various mixed finite elements for fourth-order problems are considered; error estimates of quasi-optimal or optimal order depending upon the mixed elements are derived. Implementation techniques for solving the linear system arising from these expanded mixed methods are discussed, and numerical results are presented. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 483-503, 1997
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  • 78
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    Approximation of Navier-Stokes incompressible flow using a spectral element method with a local discretization in spectral space (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 587-599 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Domain decomposition ; spectral element ; incompressible Navier Stokes ; legendre polynomials ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A spectral element technique is examined, which builds upon a local discretization within the spectral space. To approximate a given system of equations the domain is subdivided into nonoverlapping quadrilateral elements, and within each element a discretization is found in the spectral space. The difference is that the test functions are divided into the higher-order polynomials, which have zero boundaries and lower-order polynomials, which are nonzero on one boundary. The method is examined for Navier-Stokes incompressible flow for fluid flow within a driven cavity and for flow over a backstep. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 587-599, 1997
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  • 79
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    Digitale Medien
    A posteriori error estimators for the steady incompressible Navier-Stokes equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 561-574 
    Details
    ISSN: 0749-159X
    Schlagwort(e): A posteriori error estimators ; mixed finite elements methods ; Navier-Stokes equations ; automatic mesh refinement ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A residual-based a posteriori error estimator for finite element discretizations of the steady incompressible Navier-Stokes equations in the primitive variable formulation is discussed. Though the estimator is similar to existing ones, an alternate derivation is presented, involving an abstract estimate that may prove of some intrinsic value. The estimator is particularized to Hood-Taylor and modified Hood-Taylor finite elements and proved to be a global upper bound (up to a positive multiplicative constant) of the true error. Numerical examples are provided to illustrate the performance of the resulting mesh adaptation process. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 561-574, 1997
    Zusätzliches Material: 8 Ill.
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  • 80
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    Digitale Medien
    Optimal rectangular MITC finite elements for Reissner-Mindlin plates (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 575-585 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Finite elements ; plates 65N30 ; 73K10 ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In recent years a family of finite elements named mixed interpolated tensorial components (MITC) has been introduced for the numerical approximation of Reissner-Mindlin plates. The elements have been proved to be locking free. In this article, we consider the MITC rectangular finite elements and show that it is possible to reduce the number of internal degrees of freedom in the approximation of the rotation field without losing order of convergence. Our mathematical analysis is carried out combining some results for the Stokes problem with the special features of the MITC finite elements. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 575-585, 1997
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  • 81
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    Application of circuit analysis programs to systems of partial differential equations (1997)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 13 (1997), S. 601-615 
    Details
    ISSN: 0749-159X
    Schlagwort(e): network analog ; partial differential equation ; circuit analysis ; SPICE ; Burger's equation ; Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A general approach for solving systems of time domain partial differential equations using circuit analysis programs is described. The approach is then used to solve a nonlinear one-dimensional transient fluid flow problem. Using the general purpose circuit analysis program SPICE, the approach is fully implicit and should provide a convenient method for physical simulations in one dimension. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 601-615, 1997
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  • 82
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    Enslaved finite difference schemes for nonlinear dissipative PDEs (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 13-40 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show how the accuracy of a given finite difference scheme approximating a dissipative nonlinear PDE may be improved. The numerical solutions are decomposed into two parts that may be interpreted as approximating the large and small scales of the true solutions. By enslaving the small scales in terms of the larger ones, we derive a new difference scheme that is, in general, more accurate than the original scheme. The new scheme is also more computationally efficient, provided that the time derivatives of the problem are not too large. © 1996 John Wiley & Sons, Inc.
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  • 83
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    Galerkin methods for a model of population dynamics with nonlinear diffusion (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 59-73 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A numerical method is proposed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations describing age-dependent population dynamics with spatial diffusion. We use a finite difference method along the characteristic age-time direction combined with finite elements in the spatial variable. Optimal order error estimates are derived for this approximation. © 1996 John Wiley & Sons, Inc.
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  • 84
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    Mixed methods of nonlinear second-order elliptic problems in three variables (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 41-57 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Mixed finite element methods for treating the Dirichlet problem for fully nonlinear second-order elliptic operators in divergence form are extended to cover the three-dimensional case. Existence and uniqueness of the approximation are proved, and optimal error estimates in L2 are demonstrated for both the scalar and vector functions approximated by the method. Error estimates for the pressure variable are also derived in Lq; the result is optimal in order for 2 ≤ q ≤ 6 and less than optimal for 6 〈 q ≤ + ∞. Newton's method can be used to solve the nonlinear algebraic equations. © 1996 John Wiley & Sons, Inc.
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  • 85
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    A hybrid numerical method for the shallow water equations with source term (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 75-83 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In coastal oceanography there is interest in problems modeled by the shallow water equations, where variations in channel depth are accounted for by the presence of source terms. A numerical treatment for the solution of such problems is presented here, in terms of a hybrid approach, which combines a second-order TVD scheme for conservation law equations (assuming no source terms) with an eigenvector projection scheme that incorporates the effects of nonzero source terms (in regions where the bottom is not flat). For the case where an initially sharp wave profile is assumed, the progress of a wave as it traverses an estuary whose channel depth varies is calculated. Excellent numerical results are obtained. © 1996 John Wiley & Sons, Inc.
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  • 86
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    Accuracy and stability analysis of numerical schemes for the shallow water model (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 85-98 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The accuracy and stability properties of several two-level and three-level difference schemes for solving the shallow water model are analyzed by the linearized Fourier Method. The effects of explicit or implicit treatments of the gravity, Coriolis, convective and friction terms on accuracy and stability are examined. The use of Miller's properties on von Neumann polynomial plays a crucial role to resolve the tedious mathematical procedures in the Fourier analysis. As a best compromise between efficiency and stability, we recommend the semi-implicit schemes, where the surface elevation and friction terms are treated implicitly while the convective and Coriolis terms are treated explicitly. © 1996 John Wiley & Sons, Inc.
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  • 87
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    Superconvergence results for Galerkin methods for wave propagation in various porous media (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 99-122 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Finite-element methods are considered for numerically solving the equations describing wave propagation in various porous media such as inhomogeneous elastic media, fluid saturated media, composite isotropic inhomogeneous elastic media, composite anisotropic media, etc. Quasi-projection analyses based on an asymptotic expansion to high order of finite-element solutions are given to obtain error estimates in Sobolev spaces of nonpositive index for the approximate solution. Superconvergence phenomena for the finite-element methods under consideration are also investigated. © 1996 John Wiley & Sons, Inc.
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    Pointwise superconvergence of the streamline diffusion finite-element method (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 123-145 
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    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this article, we analyze the local superconvergence property of the streamline-diffusion finite-element method (SDFEM) for scalar convection-diffusion problems with dominant convection. By orienting the mesh in the streamline direction and imposing a uniformity condition on the mesh, the theoretical order of pointwise convergence is increased from O(h11/8|log h|) to O(h2|log h|). Numerical tests show that this result cannot be extended to arbitrary quasi-uniform meshes. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 7 Ill.
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    Numerical studies of optimal grid construction (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 191-206 
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    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article is concerned with the construction of optimal grids for convection dominated problems. We consider the redistribution approach to generate the optimal grids. With an optimal grid, the number of unknowns can be dramatically reduced and this generally gives a computationally efficient model. Both Galerkin finite-element and least-squares finite-element approximations are considered with mesh redistribution. Numerical results of models problems illustrating the efficiency of the minimum mesh size approach are presented. Discussions of the capabilities and limitations of the schemes are also provided. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 15 Ill.
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  • 90
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    Minimization of grid orientation effects in simulation of oil recovery processes through use of an unsplit higher order scheme (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 161-189 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present an unsplit second-order finite difference algorithm for hyperbolic conservation laws in several variables. Although the method can be directly implemented for general hyperbolic systems, we focus in this article on reducing grid orientation effects in porous media flow. In particular, we consider miscible and immiscible displacement processes. Our main concern is to develop a scheme that can easily be implemented into existing standard finite-difference-based reservoir simulators as an option to be used if grid orientation effects occur. The principle of the scheme is to build a higher order scheme to reduce numerical dispersion and that does not split the spatial operator to reduce the effect of the grid orientation. Numerical results are presented, which show that the method presented here reduces the effect of the numerical dispersion to a level that minimizes the grid orientation effects in a computationally efficient manner. © 1996 John Wiley & Sons, Inc.
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    An iterative solver for a coupled system of Helmholtz equations (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 207-219 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An iterative solver for a pair of coupled partial differential equations that are related to the Maxwell equations is discussed. The convergence of the scheme depends on the choice of two parameters. When the first parameter is fixed, the scheme is seen to be a successive under-relaxation scheme in the other parameter. A theory for convergence of the scheme is discussed for a special case of the equations, and several numerical examples are presented. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 92
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    Digitale Medien
    Numerical analysis of a mixed finite element method for a flow-transport problem (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 221-233 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider a generic flow-transport system of partial differential equations, which has wide application in the waste disposal industry. The approximation of this system, using a finite element method for the brine, radionuclides, and heat combined with a mixed finite element method for the pressure and velocity, is analyzed. Optimal order error estimates in H1 and L2 are derived. The error analysis is given with no restriction on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. © 1996 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
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  • 93
    Digitale Medien
    Digitale Medien
    A high-order compact formulation for the 3D Poisson equation (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 235-243 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this work we construct an extension to a class of higher-order compact methods for the three-dimensional Poisson equation. A superconvergent nodal rate of O(h6) is predicted, or O(h4) if the forcing function derivatives are not known exactly. Numerical experiments are conducted to verify these theoretical rates. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 94
    Digitale Medien
    Digitale Medien
    The performance of preconditioned waveform relaxation techniques for pseudospectral methods (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 245-263 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Waveform relaxation techniques for the pseudospectral solution of the heat conduction problem are discussed. The pseudospectral operator occurring in the equation is preconditioned by transformations in both space and time. In the spatial domain, domain stretching is used to more equally distribute the grid points across the domain, and hence improve the conditioning of the differential operator. Preconditioning in time is achieved either by an exponential or a polynomial transformation. Block Jacobi solutions of the systems are obtained and compared. The preconditioning in space by domain stretching determines the effectiveness of waveform relaxation in this case. Preconditioning in time is also effective in reducing the number of iterations required for convergence. The polynomial transformation is preferred, because it removes the requirement of a matrix exponential calculation in the time-stepping schemes and, at the same time, is no less effective than the direct exponential preconditioning. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 95
    Digitale Medien
    Digitale Medien
    Masthead (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996) 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690120201
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  • 96
    Digitale Medien
    Digitale Medien
    A Volterra integral type method for solving a class of nonlinear initial-boundary value problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 265-281 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: It is observed that the one-dimensional heat equation with certain nonlinear boundary conditions can be reformulated as a system of coupled Volterra integral equations. A product trapezoidal scheme is proposed for the numerical solution of this integral equation system, and some numerical experiments are given to compare the performances of this integral equation approach and the Crank-Nicholson method applied to the original initial-boundary value problem. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 8 Tab.
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  • 97
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    Digitale Medien
    Announcement (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. i 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/num.1690120202
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  • 98
    Digitale Medien
    Digitale Medien
    Nonlinear Galerkin method and two-step method for the Navier-Stokes equations (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 283-305 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article represents a new nonlinear Galerkin scheme for the Navier-Stokes equations. This scheme consists of a nonlinear Galerkin finite element method and a two-step difference method. Moreover, we also provide a Galerkin scheme. By convergence analysis, two numerical schemes have the same second-order convergence accuracy for the spatial discretization and time discretization if H is chosen such that H = O(h2/3). However, the nonlinear Galerkin scheme is simpler than the Galerkin scheme, namely, this scheme can save a large amount of computational time. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 99
    Digitale Medien
    Digitale Medien
    Numerical investigation of a trapezoidal cross-section ridge optical waveguide (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 307-314 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The mode dispersion of trapezoidal cross-section narrow ridge dielectric optical waveguides is calculated by the Weighted Residual Method (WRM). In the sloping region, the field is expressed in terms of Airy functions, thus having no arbitrariness at the boundaries. The result is compared with previously reported experimental and theoretical results. Agreement between the experimental and the predicted results is good. © 1996 John Wiley & Sons, Inc.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 100
    Digitale Medien
    Digitale Medien
    Reducing the computational requirements of the differential quadrature method (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 565-577 
    Details
    ISSN: 0749-159X
    Schlagwort(e): Mathematics and Statistics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This article shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric, if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The application of the properties of centrosymmetric and skew centrosymmetric matrices can reduce the computational effort of the DQM for calculations of the inverse, determinant, eigenvectors, and eigenvalues by 75%. This computational advantage is also demonstrated via several numerical examples. © 1996 John Wiley & Sons, Inc.
    Materialart: Digitale Medien
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