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  • CR: G1.8  (28)
  • Springer  (28)
  • American Institute of Physics
  • 2010-2014
  • 1985-1989  (28)
  • 1940-1944
  • 1986  (28)
Collection
Keywords
Publisher
  • Springer  (28)
  • American Institute of Physics
Years
  • 2010-2014
  • 1985-1989  (28)
  • 1940-1944
Year
  • 1
    Electronic Resource
    Electronic Resource
    Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 697-721 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuška paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398380
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  • 2
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    Stability and accuracy for implicit semidiscretizations of hyperbolic problems (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 221-237 
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    ISSN: 0945-3245
    Keywords: AMS (MOS) ; 65M10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we give bounds for the error constants of certain classes of stable implicit finite difference methods for first order hyperbolic equations in one space dimension. We consider classes of methods that user downwind ands upwind points in the explicit part andR downwind andS upwind points in the implicit part, respectively, and that are of optimal orderp=min (r+R+s+S, 2(r+R+1), 2(s+S)). In some cases the error constant of interpolatory methods [5] can be improved. The results are proved via the order star technique. They are further used to determine methods of optimal order that are stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389870
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  • 3
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    Approximation numérique du cisaillement transverse dans les plaques minces en flexion (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 281-302 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary After a brief review of the main numerical methods for approximating the bending of plates, we discuss the difficulties met in the computation of the transverse shearing stress. Introducing mixed variational formulations, we propose several numerical schemes leading to a good approximation of this quantity. Finally, the opportunity of using such schemes is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389476
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  • 4
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    On the construction of optimal mixed finite element methods for the linear elasticity problem (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 447-462 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The mixed finite element method for the linear elasticity problem is considered. We propose a systematic way of designing methods with optimal convergence rates for both the stress tensor and the displacement. The ideas are applied in some examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389651
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  • 5
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    Stream vectors in three dimensional aerodynamics (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 561-589 
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    ISSN: 0945-3245
    Keywords: AMS (MOS):65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This work deals with the decomposition of a vector fieldu intou=∇×ψ+∇φ. Non homogeneous boundary conditions on ψ or φ are investigated; applications to the computation of inviscid flows are given; finally a conforming finite element implementation is studied and tested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389451
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  • 6
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    On the multi-level splitting of finite element spaces (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 379-412 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10, 65F35, 65N20, 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we analyze the condition number of the stiffness matrices arising in the discretization of selfadjoint and positive definite plane elliptic boundary value problems of second order by finite element methods when using hierarchical bases of the finite element spaces instead of the usual nodal bases. We show that the condition number of such a stiffness matrix behaves like O((log κ)2) where κ is the condition number of the stiffness matrix with respect to a nodal basis. In the case of a triangulation with uniform mesh sizeh this means that the stiffness matrix with respect to a hierarchical basis of the finite element space has a condition number behaving like $$O\left( {\left( {\log \frac{1}{h}} \right)^2 } \right)$$ instead of $$O\left( {\left( {\frac{1}{h}} \right)^2 } \right)$$ for a nodal basis. The proofs of our theorems do not need any regularity properties of neither the continuous problem nor its discretization. Especially we do not need the quasiuniformity of the employed triangulations. As the representation of a finite element function with respect to a hierarchical basis can be converted very easily and quickly to its representation with respect to a nodal basis, our results mean that the method of conjugate gradients needs onlyO(log n) steps andO(n log n) computer operations to reduce the energy norm of the error by a given factor if one uses hierarchical bases or related preconditioning procedures. Heren denotes the dimension of the finite element space and of the discrete linear problem to be solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389538
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  • 7
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    A remark on theL ∞ bounds of the Ritz operator associated with a finite element approximation (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 529-544 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For the elliptic operatorA of second order, its finite element approximationA h is considered by piecewise linear trial functions. AnL ∞ bound on the Ritz operator is shown by Stampacchia's method, which implies a discrete elliptic-Sobolev inequality forA h.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389704
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  • 8
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    Analysis of the Kleiser-Schumann method (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 217-243 
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    ISSN: 0945-3245
    Keywords: AMS(MOS) 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Kleiser-Schumann algorithm for the approximation of the Stokes problem by Fourier/Legendre polynomials is analized. Stability when the degree of the polynomials increases is established, whereas error estimates in Sobolev spaces are proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390431
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  • 9
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    Finite element solution of nonlinear elliptic problems (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 451-475 
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    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The study of the finite element approximation to nonlinear second order elliptic boundary value problems with mixed Dirichlet-Neumann boundary conditions is presented. In the discretization variational crimes are commited (approximation of the given domain by a polygonal one, numerical integration). With the assumption that the corresponding operator is strongly monotone and Lipschitz-continuous and that the exact solutionu∈H 1(Ω), the convergence of the method is proved; under the additional assumptionu∈H 2(Ω), the rate of convergenceO(h) is derived without the use of Green's theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396664
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  • 10
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    On the finite element approximation of a cascade flow problem (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 655-684 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 76-08 ; 76G99 ; 76N10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The finite element analysis of a cascade flow problem with a given velocity circulation round profiles is presented. The nonlinear problem for the stream function with nonstandard boundary conditions is discretized by conforming linear triangular elements. We deal with the properties of the discrete problem and study the convergence of the method both for polygonal and nonpolygonal domains, including the effect of numerical integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398378
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  • 11
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    Optimal control of a Stefan problem with state-space constraints (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 723-744 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K10 ; 65M60 ; 49A22 ; 35K65 ; CR: G1.8 ; G1.2
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An optimal control problem with state-space constraints for a multidimensional Stefan problem in an enthalpy formulation with nonlinear boundary conditions is investigated. The existence and stability of a solution of the optimal control problem is shown providing a set of admissible controls is compact. Also, a boundary observation is admitted. The original problem is then approximated by using a penalty-function method, finite-element method in space and backward Euler formula in time. The convergence of the approximate optimal controls is proved. Moreover, an example for non-stability of the penalty-function method inL p spaces is constructed. Finally, numerical results of an illustrative example are presented.
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    URL: http://dx.doi.org/10.1007/BF01398381
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  • 12
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    A nonconforming combined method for solving Laplace's boundary value problems with singularities (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 475-497 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For solving Laplace's boundary value problems with singularities, a nonconforming combined approach of the Ritz-Galerkin method and the finite element method is presented. In this approach, singular functions are chosen to be admissible functions in the part of a solution domain where there exist singularities; and piecewise linear functions are chosen to be admissible functions in the rest of the solution domain. In addition, the admissible functions used here are constrained to be continuous only at the element nodes on the common boundary of both methods. This method is nonconforming; however, the nonconforming effect does not result in larger errors of numerical solutions as long as a suitable coupling strategy is used. In this paper, we will develop such an approach by using a new coupling strategy, which is described as follows: IfL+1=O(|lnh|), the average errors of numerical solutions and their generalized derivatives are stillO(h), whereh is the maximal boundary length of quasiuniform triangular elements in the finite element method, andL+1 is the total number of singular admissible functions in the Ritz-Galerkin method. The coupling relation,L+1=O(|lnh|), is significant because only a few singular functions are required for a good approximation of solutions.
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    URL: http://dx.doi.org/10.1007/BF01389701
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  • 13
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    Superconvergence for a mixed finite elmenent method for elastic wave propagation in a plane domain (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 189-202 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A higher order mixed finite element method is introduced to approximate the solution of wave propagation in a plane elastic medium. A quasi-projection analysis is given to obtain error estimates in Sobolev spaces of nonpositive index. Estimates are given for difference quotients for a spatially periodic problem and superconvergence results of the same type as those of Bramble and Schatz for Galerkin methods are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389623
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  • 14
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    Multi-grid methods for Hamilton-Jacobi-Bellman equations (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 239-254 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we develop multi-grid algorithms for the numerical solution of Hamilton-Jacobi-Bellman equations. The proposed schemes result from a combination of standard multi-grid techniques and the iterative methods used by Lions and mercier in [11]. A convergence result is given and the efficiency of the algorithms is illustrated by some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389627
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  • 15
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    Numerical computation of least constants for the Sobolev inequality (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 607-616 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Least constantsc for the well-known Sobolev inequality ∥f∥∞≦c∥f∥ m, G ,f∈H m (G) are obtained in closed form by a reproducing kernel technique, where the Sobolev spaceH m (G) for a domainG in ℝ n is defined as the completion ofC m (G) with respect to the Sobolev norm given by $$\left\| f \right\|_{m, G}^2 = \sum\limits_{\left| p \right| \leqq m} {\left\| {D^p f} \right\|^2 } $$ , where ‖ ‖ is the norm ofL 2 (G) and ‖ ‖∞ is the supremum norm onG. Numerical values for the case whereG is the ℝ n are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399684
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  • 16
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    Asymptotic error expansion and Richardson extranpolation for linear finite elements (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 11-37 
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    ISSN: 0945-3245
    Keywords: AMS(MOS):65N300 ; 65B05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The elliptic Ritz projection with linear finite elements is shown to admit asymptotic error expansions on certain uniform meshes. This justifies the application of Richardson extrapolation for increasing the accuracy.
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    URL: http://dx.doi.org/10.1007/BF01389427
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  • 17
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    Approximation of the solution of a fourth order boundary value problem with nonsmooth coefficient (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 125-145 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A class of generalized finite element methods for the approximate solution of fourth order two point boundary value problem with nonsmooth coefficient is presented. The methods are based on the use of problem dependentL-splines incorporating the nonsmoothness of the coefficient. Stability is proved and optimal error estimates in theH 2 norm are derived for the solution and postprocessed solution, under the assumption that the coefficient is of bounded variation. The relation of these methods to mixed methods is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390426
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  • 18
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    Finite element approximation of the Dirichlet problem using the boundary penalty method (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 343-366 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper considers a finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation,Au=f, in a region Ω ⊂ ℝn (n=2 or 3) by the boundary penalty method. If the finite element space defined overD h , a union of elements, has approximation powerh K in theL 2 norm, then (i) for Ω≡D h convex polyhedral, we show that choosing the penalty parameter ε≡h λ with λ≧K yields optimalH 1 andL 2 error bounds ifu∈H K+1 (Ω); (ii) for ϖΩ being smooth, an unfitted mesh $$(\Omega \subseteq D^h )$$ and assumingu∈H K+2 (Ω) we improve on the error bounds given by Babuska [1]. As (ii) is not practical we analyse finally a fully practical piecewise linear approximation involving domain perturbation and numerical integration. We show that the choice λ=2 yields an optimalH 1 and interiorL 2 rate of convergence for the error. A numerical example is presented confirming this analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389536
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  • 19
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    A new family of mixed finite elements in ℝ3 (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 57-81 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We introduce two families of mixed finite element on conforming inH(div) and one conforming inH(curl). These finite elements can be used to approximate the Stokes' system.
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    URL: http://dx.doi.org/10.1007/BF01389668
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  • 20
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    Finite difference approximations to the Dirichlet problem for elliptic systems (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 227-237 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Dirichlet problem foru=(u 1,...,u n ) $$\Delta u + f(x,u) = 0in\Omega ,u = 0on\Gamma = \partial \Omega $$ wheref=(f 1,...,f n ), is discretized in the usual way (h mesh size): $$\Delta ^h u + f(x,u) = 0in\Omega _h ,u = 0on\Gamma _h $$ We consider variousmonotone, convergent iterative schemes. Among others, they can be used, together with estimation theorems for upper and lower solutions, to show uniqueness for solutions of (2). Numerical results are given for the system $$\Delta u + u(a - bu - c\upsilon ) = 0,\Delta \upsilon + \upsilon (d - eu - f\upsilon ) = 0$$ from mathematical biology (two competing species). It is shown that there is a unique positive solution for certain values of the positive parametersa,..., f. This result is crucial for the asymptotic behavior of solutions of the corresponding parabolic system ast→∞.
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    URL: http://dx.doi.org/10.1007/BF01389626
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  • 21
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    An asymptotic finite element method for improvement of solutions of boundary layer problems (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 425-438 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(εn+1) (where ε is the “small” parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes.
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    URL: http://dx.doi.org/10.1007/BF01389540
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  • 22
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    Analysis of a non-linear difference scheme in reaction-diffusion (1986)
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    Numerische Mathematik 49 (1986), S. 511-527 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65MO5 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A nonlinear partial difference equation resulting from discretising in space and time the parabolic reaction diffusion equation, which models the spruce budworm problem, is analysed and accuracy estimates obtained for solutions over afinite time range and ast→∞. Although the analysis is restricted to the logistic model in one space dimension, the techniques and comparison principles developed in the paper should prove useful in assessing the merits of numerical solutions of other nonlinear parabolic difference equations.
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    URL: http://dx.doi.org/10.1007/BF01389703
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  • 23
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    A convergence analysis of hopscotch methods for fourth order parabolic equations (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 275-290 
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    ISSN: 0945-3245
    Keywords: AMS(MOS):65M10, 65M20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Consider the ODE (ordinary differential equation) that arises from a semi-discretization (discretization of the spatial coordinates) of a first order system form of a fourth order parabolic PDE (partial differential equation). We analyse the stability of the finite difference methods for this fourth order parabolic PDE that arise if one applies the hopscotch idea to this ODE. Often the error propagation of these methods can be represented by a three terms matrix-vector recursion in which the matrices have a certain anti-hermitian structure. We find a (uniform) expression for the stability bound (or error propagation bound) of this recursion in terms of the norms of the matrices. This result yields conditions under which these methods are strongly asymptotically stable (i.e. the stability is uniform both with respect to the spatial and the time stepsizes (tending to 0) and the time level (tending to infinity)), also in case the PDE has (spatial) variable coefficients. A convergence theorem follows immediately.
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    URL: http://dx.doi.org/10.1007/BF01389630
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    Regions of stability, equivalence theorems and the Courant-Friedrichs-Lewy condition (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 319-329 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The celebrated CFL condition for discretizations of hyperbolic PDEs is shown to be equivalent to some results of Jeltsch and Nevanlinna concerning regions of stability ofk-step,m-stage linear methods for the integration of ODEs. We characterize the methods for the numerical integration of the model equation,u t=u x which are weakly stable when the mesh-ratio takes the maximum value allowed by the CFL condition. We provide new equivalence theorems between stability and convergence, which improve on the classical results.
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    URL: http://dx.doi.org/10.1007/BF01389633
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    Theh,p andh-p versions of the finite element method in 1 dimension (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 577-612 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper is the first one in the series of three which are addressing in detail the properties of the three basic versions of the finite element method in the one dimensional setting The main emphasis is placed on the analysis when the (exact) solution has singularity of xα-type. The first part analyzes thep-version, the second theh-version and generalh-p version and the final third part addresses the problems of the adaptiveh-p version.
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    URL: http://dx.doi.org/10.1007/BF01389733
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  • 26
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    A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 45-55 
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    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J15, 65N15 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu h in the norm of a suitable space $$Z \subseteq X \cap Y$$ . Sufficient conditions for the uniform boundedness ‖u h ‖ Z =O(1) ash→0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain $$\Omega \subseteq \mathbb{R}^n $$ . The approximating subspaces are finite element spaces. Especially the caseX=W 0 m, p (Ω), 1〈p〈∞,Y=W 0 m. 2 (Ω),Z=W 0 m. max (2,p) (Ω)∩Wm, ∞ (Ω) is treated. Some examples for 1〈p〈2 are considered. Forp≧2 a refined technique is introduced in the author's paper [7].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389667
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  • 27
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    Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 147-169 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The present paper deals with the mathematical and the numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is proved to be well-posed, consistent mixed finite element approximations are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-directions time-integrations of this stress evolution problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390427
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  • 28
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    Electronic Resource
    Mixed finite element approximation of the vector potential (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 685-695 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a mixed finite element approximation of the three dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddlepoint formulation of the essential boundary conditions. In particular, this avoids the wellknown Babuška paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398379
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