ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles  (123)
  • CR: G1.8  (100)
  • Wetlands
  • sediment
  • 1985-1989  (123)
  • Mathematics  (101)
  • Energy, Environment Protection, Nuclear Power Engineering  (22)
Collection
  • Articles  (123)
Source
Keywords
Publisher
Years
Year
Topic
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Applications of fixed-point methods to discrete variational and quasi-variational inequalities (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 631-654 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20, 65N10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, discrete analogues of variational inequalities (V.I.) and quasi-variational inequalities (Q.V.I.), encountered in stochastic control and mathematical physics, are discussed. It is shown that those discrete V.I.'s and Q.V.I.'s can be written in the fixed point formx=Tx such that eitherT or some power ofT is a contraction. This leads to globally convergent iterative methods for the solution of discrete V.I.'s and Q.V.I.'s, which are very suitable for implementation on parallel computers with single-instruction, multiple-data architecture, particularly on massively parallel processors (M.P.P.'s).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400174
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Compactness method in the finite element theory of nonlinear elliptic problems (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 147-163 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Finite element approximation of a nonlinear elliptic pseudomonotone second-order boundary value problem in a bounded nonpolygonal domain Ω with mixed Dirichlet-Neumann boundary conditions is studied. In the discretization we approximate the domain Ω by a polygonal one, use linear conforming triangular elements and evaluate integrals by numerical quadratures. We prove the solvability of the discrete problem and on the basis of compactness properties of the corresponding operator (which is not monotone in general) we prove the convergence of approximate solutions to an exact weak solutionu∈H 1 Ω). No additional assumption on the regularity of the exact solution is needed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398687
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Extrapolation techniques for reducing the pollution effect or reentrant corners in the finite element method (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 539-564 
    Details
    ISSN: 0945-3245
    Keywords: AMS(OMS): 65N30, 65B05, 73K25 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Standard finite element schemes applied to boundary value problems on domains with reentrant corners suffer from a global loss of accuracy caused by the influence of the corner singularities. For a model situation, it is shown that this pollution effect can be completely described in terms of an asymptotic error expansion with respect to fractional powers of the mesh size parameter. This provides the basis of an extrapolation procedure which recovers the full order of accuracy for the solution as well as for the corresponding stress intensity factors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400891
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Approximation by finite differences of the propagation of acoustic waves in stratified media (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 655-702 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we analyze the approximation of acoustic waves in a two layered media by a finite diffrences variational scheme. We examine in particular the approximation of the guided waves. We point out the existence of purely numerical parasitic phenomena and quantify the numerical dispersion relative to guided waves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396488
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A generalization of the schwarz alternating method to an arbitrary number of subdomains (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 61-81 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 or 65J10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We give a generalization of the Schwarz alternating method to an arbitrary number of subdomains. As applications, we prove that the method converges for the main second-order boundary value problems, as well as for the system of linear elasticity. For the Dirichlet problems it is proved that the method converges geometrically and some numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395872
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    L ∞-Error estimate for an approximation of a parabolic variational inequality (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 557-565 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Almost optimalL ∞-convergence of an approximation of a variational inequality of parabolic type is proved under regularity assumptions which are met by the solution of a one phase Stefan problem. The discretization employs piecewise linear finite elements in space and the backward Euler scheme in time. By means of a maximum principle the problem is reduced to an error estimate for an auxiliary parabolic equation. The latter bound is obtained by using the smoothing property of the Galerkin method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408576
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Numerical solution for exterior problems (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 87-101 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We solve the Helmholtz equation in an exterior domain in the plane. A perfect absorption condition is introduced on a circle which contains the obstacle. This boundary condition is given explicitly by Bessel functions. We use a finite element method in the bounded domain. An explicit formula is used to compute the solution out of the circle. We give an error estimate and we present relevant numerical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399696
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Mixed finite elements for second order elliptic problems in three variables (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 237-250 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two families of mixed finite elements, one based on simplices and the other on cubes, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. These spaces are analogues of those introduced by Brezzi, Douglas, and Marini in two space variables. Error estimates inL 2 andH −s are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396752
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Error analysis for absorbing boundary conditions (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 459-467 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35L20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An estimate is derived for the error committed by the introduction of artificial boundaries and corresponding artificial boundary conditions when solving wave equations on unbounded domains. The estimate has two terms. One is proportional to the largest reflection coefficient for the artificial boundary condition, the maximum taken only on those rays which appear in the computation. The second term is proportional to 1/k wherek is a measure of the average frequency present in the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397547
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    On the numerical approximation of finite speed diffusion problems (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 97-105 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Lagrangian formulations for the Cauchy problems for the generalized-heat and porous-media equations are introduced and equivalence and existence results discussed. Efficient interface tracking finite difference and finite element discretizations of the Lagrangian formulation are discussed. Mixed Euler-Lagrange formulations for mixed problems and the one phase Stefan problem are presented. Numerical experiments are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395879
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Convergence of the multilevel Full Approximation Scheme including theV-cycle (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 663-686 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The multilevel Full Approximation Scheme (FAS ML) is a well-known solver for nonlinear boundary value problems. In this paper we prove local quantitative convergence statements for a class of FAS ML algorithms in a general Hilbertspace setting. This setting clearly exhibits the structure of FAS ML. We prove local convergence of a nested iteration for a rather concrete class of FAS ML algorithms in whichV-cycles and only one Jacobilike pre- and post-smoothing on each level are used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397135
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    Electronic Resource
    Electronic Resource
    On the convergence of finite-difference schemes for parabolic equations with variable coefficients (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 395-404 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS: 65N10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the convergence of the finite-difference schemes for the first initial-boundary value problem for linear second-order parabolic equations with variable coefficients. Using the bilinear version of the Bramble-Hilbert lemma we obtain estimate of convergence, in discreteW 2 1, 1/2 norm, compatible with the smoothness of generalized solutionu∈W 2 λ, λ/2 (Q) (1〈λ≦3) and coefficients of equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396321
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    Electronic Resource
    Electronic Resource
    Konvergenzaussagen für Kollokationsverfahren bei elliptischen Randwertaufgaben (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 619-637 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We examine the convergence of collocation with polynomials for elliptic problems. The general theory is imbedded in theL p -theory from which known results of existence and regularity are adopted. Convergence results are deduced in the cases of periodic, Dirichlet and mixed boundary conditions. It becomes obvious that the order of convergence essentially depends on the smoothness of the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396486
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    Electronic Resource
    Electronic Resource
    Numerical analysis of the weighted particle method applied to the semiconductor Boltzmann equation (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 599-618 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65P05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The semiconductor Boltzmann equation involves an integral operator, the kernel of which is a measure supported by a surface. This feature introduces some singularities of the exact solution, which makes the numerical approximation of this equation difficult. This paper is devoted to the error analysis of the weighted particle method (introduced by Mas-Gallic and Raviart [14]) applied to the space homogeneous semiconductor Boltzmann equation. The results are commented in view of the practical use of the method. This paper is closely related to [12], where results of numerical simulations on both test and real problems are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398918
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    Electronic Resource
    Electronic Resource
    Finite element approximation of viscoelastic progressively incompressible flows (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 43-66 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K19 ; 65N30 ; 73F05 ; 76A05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary To avoid any numerical locking in the finite element approximation of viscoelastic flow problems, we propose a three-field approximation of this problem. This approximation, which involves velocities, stresses, and pressures is proved to converge for all times. In the proof, we also obtain convergence results for the three-fields finite element approximation of incompressible elasticity problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395777
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    Spectral methods with sparse matrices (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 25-41 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Spectral methods employ global polynomials for approximation. Hence they give very accurate approximations for smooth solutions. Unfortunately, for Dirichlet problems the matrices involved are dense and have condition numbers growing asO(N 4) for polynomials of degree ≦N in each variable. We propose a new spectral method for the Helmholtz equation with a symmetric and sparse matrix whose condition number grows only asO(N 2). Certain “algebraic spectral multigrid methods” can be efficiently used for solving the resulting system. Numerical results are presented which show that we have probably found the most effective solver for spectral systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395776
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    The frequency decomposition multi-grid method (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 229-245 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new variant of the multi-grid algorithms is presented. It uses multiple coarse-grid corrections with particularly associated prolongations and restrictions. In this paper the robustness with respect to anisotropic problems is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01409786
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    An optimal order multigrid method for biharmonic,C 1 finite element equations (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 613-624 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65F10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we study a special multigrid method for solving large linear systems which arise from discretizing biharmonic problems by the Hsieh-Clough-Tocher,C 1 macro finite elements or several otherC 1 finite elements. Since the multipleC 1 finite element spaces considered are not nested, the nodal interpolation operator is used to transfer functions between consecutive levels in the multigrid method. This method converges with the optimal computational order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396347
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    Some new families of finite elements for the stokes equations (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 827-838 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We introduce a way of using the mixed finite element families of Raviart, Thomas and Nedelec [13, 14], and Brezzi et al. [5–7], for constructing stable and optimally convergent discretizations for the Stokes problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405291
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    Domain decomposition methods for pseudo spectral approximations (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 329-344 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Multidomain pseudo spectral approximations of second order boundary value problems in one dimension are considered. The equation is collocated at the Chebyshev nodes inside each subinterval. Different patching conditions at the interfaces are analyzed. Results of stability and convergence are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398883
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    Multiple discrete solutions of the incompressible steady-state Navier-Stokes equations (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 31-50 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 6D05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper discusses the computation of multiple solutions of various discretizations of the steady state incompressible Navier-Stokes equations. Solution paths (α,R) satisfying the discrete system of equationsH(α,R)=0, where α represents the discrete flow field andR is the Reynolds number, are computed using a pseudo arc-length continuation procedure. For flows over the back end of an axially symmetric body with a cusped tail in a coaxial circular cylinder, the solution paths often exhibit “hairpin” turning points. Dependence of the paths on the mesh spacing and various selections for the discretizations of the convective and diffusive terms are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395877
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    A new family of stable elements for nearly incompressible elasticity based on a mixed Petrov-Galerkin finite element formulation (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 123-141 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS):65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Adding to the classical Hellinger Reissner formulation another residual form of the equilibrium equation, a new Petrov-Galerkin finite element method is derived. It fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations, including equal-order discontinuous stress and continuous displacement interpolations which are unstable within the Galerkin approach. Error estimates are presented using the Babuška-Brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395881
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    Stabilized mixed methods for the Stokes problem (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 225-235 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The solution of the Stokes problem is approximated by three stabilized mixed methods, one due to Hughes, Balestra, and Franca and the other two being variants of this procedure. In each case the bilinear form associated with the saddle-point problem of the standard mixed formulation is modified to become coercive over the finite element space. Error estimates are derived for each procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395886
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    A constructive method for deriving finite elements of nodal type (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 701-738 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we propose an algorithm to derive nodal methods corresponding to various two and three-dimensional nonconforming and mixed finite elements. We show that this algorithm can be used to obtain several classical schemes as well as some more recently developed schemes, and that it leads to a simple proof of unisolvence for these methods. Finally we use our method to obtain a three dimensional nodal scheme of BDM type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397137
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    Computable bounds for eigenvalues and eigenfunctions of elliptic differential operators (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 201-223 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N25 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We are concerned with bounds for the error between given approximations and the exact eigenvalues and eigenfunctions of self-adjoint operators in Hilbert spaces. The case is included where the approximations of the eigenfunctions don't belong to the domain of definition of the operator. For the eigenvalue problem with symmetric elliptic differential operators these bounds cover the case where the trial functions don't satisfy the boundary conditions of the problem. The error bounds suggest a certain defectminization method for solving the eigenvalue problems. The method is applied to the membrane problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396975
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    A second order splitting method for the Cahn-Hilliard equation (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 575-590 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A semi-discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary, fourth order in space, Cahn-Hilliard equation. Optimal order error bounds are derived in various norms for an implementation which uses mass lumping. The continuous problem has an energy based Lyapunov functional. It is proved that this property holds for the discrete problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396363
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    Preconditioning indefinite discretization matrices (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 719-734 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10, 65N20, 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The finite element discretization of many elliptic boundary value problems leads to linear systems with positive definite and symmetric coefficient matrices. Many efficient preconditioners are known for these systems. We show that these preconditioning matrices can also be used for the linear systems arising from boundary value problems which are potentially indefinite due to lower order terms in the partial differential equation. Our main tool is a careful algebraic analysis of the condition numbers and the spectra of perturbed matrices which are preconditioned by the same matrices as in the unperturbed case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396490
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    Analysis of a damped nonlinear multilevel method (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 225-246 
    Details
    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 present a new algorithm that is obtained by introducing a damping parameter in the classical Nonlinear Multilevel Method. We analyse this Damped Nonlinear Multilevel Method. In particular, we prove global convergence and local efficiency for a suitable class of problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01406516
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    A posteriori error estimators for the Stokes equations (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 309-325 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N15, 65N30, 76D05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390056
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    Finite element variational crimes in parabolic-elliptic problems (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 343-376 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M60 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The study of a completely discretized variational problem corresponding to a nonlinear second order parabolic-elliptic initial-boundary value problem with an initial value only inL 2 is presented. The discretization in time is done by the Euler backward method, the discretization in space by the finite element method with linear functions on triangular elements. The changes in domain are taken into account. The convergence and the unconditional stability of the method is proved under the assumption that the boundary ∂Ω is piecewise of classC 3 and the forma(v, w) has a potential and is strongly monotone and Lipschitz continuous. As a by-product the existence and uniqueness theorem is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390058
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    A relaxation procedure for domain decomposition methods using finite elements (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 575-598 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present the convergence analysis of a new domain decomposition technique for finite element approximations. This technique was introduced in [11] and is based on an iterative procedure among subdomains in which transmission conditions at interfaces are taken into account partly in one subdomain and partly in its adjacent. No global preconditioner is needed in the practice, but simply single-domain finite element solvers are required. An optimal strategy for an automatic selection of a relaxation parameter to be used at interface subdomains is indicated. Applications are given to both elliptic equations and incompressible Stokes equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398917
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    The numerical computation of compressed states of nonlinearly elastic anisotropic plates (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 93-107 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we study the numerical computation of the compressed states of nonlinearly elastic anisotropic circular plates. The singular boundary value problem giving the compressed states depend parametrically on the applied pressure at the edge of the plate. We give a finite difference approximation of this problem and derive bounds for the global error by using the techniques of Brezzi, Rappaz and Raviart for the finite dimensional approximation of nonlinear problems. Some numerical results are given for a class of materials whose constitutive functions reflect the standard Poisson ratio effects.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395780
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    Control of stefan problems by means of linear-quadratic defect minimization (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 429-442 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65P05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the following problem: To influence a heat conduction process in such a way that the conductor melts in a prescribed manner. Since we treat a linear auxiliary problem, it suffices to deal with a linear-quadratic defect minimization problem with linear restrictions, where we use splines or polynomials as approximation spaces. In case of exact controllability we derive various order of convergence estimates, which we discuss for some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389495
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    A finite element lumped mass scheme for solving eigenvalue problems of circular arches (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 499-504 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This study is a continuation of a previous paper [4] in which the numerical results are given by using single precision arithmetic. In this paper, we show the numerical results which experess the sharper convergence properties than those of [4], by using double precision arithmetic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389655
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    Error estimates for a semi-explicit numerical scheme for Stefan-type problems (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 165-185 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A parabolic problem of the following form is considered (1) $$\frac{\partial }{{\partial t}}\left[ {a\vartheta + w} \right] - \Delta \vartheta = f$$ (2) $$w \varepsilon \Lambda (\vartheta ),$$ wherea is a positive constant,f is a datum and λ is a maximal monotone graph. This system contains the (weak formulation of the)Stefan problem as a particular case. Here the problem (1), (2) is approximated by coupling (1) with therelaxed equation (3) $$\varepsilon \frac{{\partial w}}{{\partial t}} + \Lambda ^{ - 1} (w) \mathrel\backepsilon \vartheta (\varepsilon : constant 〉 0).$$ The problem (1), (3) is then discretized in time by thesemi-explicit scheme (4) $$a\frac{{\vartheta ^n - \vartheta ^{n - 1} }}{\tau } + \frac{{w^n - w^{n - 1} }}{\tau } - \Delta \vartheta ^n = f^n$$ (5) $$\varepsilon \frac{{w^n - w^{n - 1} }}{\tau } + \Lambda ^{ - 1} (w^n ) \mathrel\backepsilon \vartheta ^{n - 1} ;$$ a finite element space discretization and quadrature formulae are then introduced. Thus at each time-step (5) is replaced by a finite number ofindependent algebraic equations, which can be solved with respect to the barycentral values ofw n ; then (4) is reduced to alinear system of algebraic equations having as unknowns the nodal values of ϑ n . Assuming the condition τ/ε≦a, the fully discrete scheme is stable and its solution converges to that of (1), (2). Error estimates are proved. The results of some numerical experiments are discussed; they show that the present method is faster than other classical procedures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398688
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Counterexamples to a stability barrier (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 301-316 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider multistep difference schemes for the linear, constant coefficient advection equationu t=cux. In the last section of Strang [5], a barrier for the order of stable schemes has been given which was independent of the number of time levels. Here we give two types of counterexamples to this barrier. The first type consists of formulas of highest possible order to a given stencil, which are stable for small positive Courant numbers. Further a formula is given where one does not insist on having the highest possible order for the stencil and uses the gained freedom to ensure stability for small positive and negative Courant numbers. In addition, an explicit formula is derived for the schemes of highest possible order when stability is disregarded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398881
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    A quantitative discrete H2-regularity estimate for the Shortley-Weller scheme in convex domains (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 523-537 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N99 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the discreteH 2-regularity properties of the Shortley-Weller discretization of Poisson's equation (with homogeneous Dirichlet boundary condition) in bounded convex domains Ω⊂ℝ2. It is shown that the regularity constant is 1 independent of the mesh sizeh if theH 2-seminorm is defined in a way assigning less weight to the (unsymmetric) differences near the boundary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400890
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    A new mixed formulation for elasticity (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 13-30 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 73C35 ; 73K25 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We propose a new mixed variational formulation for the equations of linear elasticity. It does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395876
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 237-254 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We set up a framework for analyzing mixed finite element methods for the plate problem using a mesh dependent energy norm which applies both to the Kirchhoff and to the Mindlin-Reissner formulation of the problem. The analysis techniques are applied to some low order finite element schemes where three degrees of freedom are associated to each vertex of a triangulation of the domain. The schemes proceed from the Mindlin-Reissner formulation with modified shear energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395887
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    On the boundary element method for some nonlinear boundary value problems (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 299-314 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Here we analyse the boundary element Galerkin method for two-dimensional nonlinear boundary value problems governed by the Laplacian in an interior (or exterior) domain and by highly nonlinear boundary conditions. The underlying boundary integral operator here can be decomposed into the sum of a monotoneous Hammerstein operator and a compact mapping. We show stability and convergence by using Leray-Schauder fixed-point arguments due to Petryshyn and Nečas. Using properties of the linearised equations, we can also prove quasioptimal convergence of the spline Galerkin approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404466
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    The convergence of a direct BEM for the plane mixed boundary value problem of the Laplacian (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 145-165 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 45F15, 45L10, 65N30, 65R20, 65N15 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the convergence analysis of a direct boundary elecment method for the mixed boundary value problem for Laplace equation in a smooth plane domain is given. The method under consideration is based on the collocation solution by constant elements of the corresponding system of boundary integral equations. We prove the convergence of this method, provide asymptotic error estimates for the BEM-solution and give some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396971
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    Pointwise accuracy of a finite element method for nonlinear variational inequalities (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 601-618 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N15, 65N30, 35J85, 35R35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Consider the following quasilinear elliptic PDE, which is equivalent to a nonlinear variational inequality: −divF(▿u)+β(u)∋f. Here β is a singular maximal monotone graph and the nonlinear differential operator is only assumed to be monotone; surfaces of prescribed mean curvature over obstacles may thus be viewed as relevant examples. The numerical approximation proposed in this paper consists of combining continuous piecewise linear finite elements with a preliminary regularization of β. The resulting scheme is shown to be quasi-optimally accurate inL ∞. The underlying analysis makes use of both a topological technique and a sharpL p -duality argument.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396485
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    The convergence of two numerical schemes for the Navier-Stokes equations (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 33-60 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper deals with some convergence/stability results concerning two numerical methods for solving the incompressible nonstationary Navier-Stokes equations. The algorithms are of a particular kind in what regards time discretization (more precisely, of the Peaceman-Rachford and the Strang type resp.), and have been obtained by modifying slightly the numerical treatment of the nonlinear terms in other schemes due to Glowinski et al. (1980). We first describe the full discretization of the homogeneous Dirichlet problem using a (general) external approximation of the spatial functional spaces involved (a particular and simple choice of such an approximation is the standardP 2-Lagrange finite element for the velocity field when the fluid is bidimensional). Then we establish and prove convergence and stability and make some comments on the numerical treatment of other (generally nonhomogeneous) boundary conditions. The theoretical results show that the schemes are (at least) conditionally stable and convergent, which justifies the success of Glowinski's methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395871
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 521-544 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 65N10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider first the initial-boundary value problem for the parabolic equation $$\varepsilon y_{xx} + a(x,t)y_x - b(x,t)y - d(x,t)y_t = f(x,t)$$ on [0, 1]×[0,T], where 0〈ɛ≦1 anda, b, d, f are smooth witha〉0,b〉0 andd〉0. Bounds ony and its derivatives are obtained under certain compatibility assumptions on the data. We examine a family of difference schemes for this problem which is exponentially fitted in thex-variable and uses classical differencing in thet-variable, on rectangular grids which are arbitrarily spaced in both thex andt directions. Under a Courant-Friedrichs-Lewy-type condition, the errors at the grid points are shown to be bounded byC(H+K), whereH(K) is the maximum mesh width in thex(t) direction andC is a constant independent of ɛ,H andK. The corresponding result for a two-point boundary value problem is also derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398914
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    Pointwise error estimates for a streamline diffusion finite element scheme (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 707-719 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Pointwise error estimates for a streamline diffusion scheme for solving a model convection-dominated singularly perturbed convection-diffusion problem are given. These estimates improve pointwise error estimates obtained by Johnson et al.[5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405198
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    Point approximation of a space-homogeneous transport equation (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 763-774 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 45K05 ; 65C20 ; 82A70 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405287
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    On finite element approximation in theL ∞-norm of variational inequalities (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 45-57 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS)-65N30, 49D20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We are interested in the approximation in theL ∞-norm of variational inequalities with non-linear operators and somewhat irregular obstacles. We show that the order of convergence will be the same as that of the equation associated with the non-linear operator if the discrete maximum principle is verified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389875
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 139-157 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A semidiscrete Galerkin finite element method is defined and analyzed for nonlinear evolution equations of Sobolev type in a single space variable. Optimal orderL p error estimates are derived for 2≦p≦∞. And it is shown that the rates of convergence of the approximate solution and its derivative are one order better than the optimal order at certain spatial Jacobi and Gauss points, respectively. Also the standard nodal superconvergence results are established. Futher, it is considered that an a posteriori procedure provides superconvergent approximations at the knots for the spatial derivatives of the exact solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389881
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    Approximation of a bending plate problem with a boundary unilateral constraint (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 435-458 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study a variational formulation of the unilaterally supported bent plate problem and we analyze the approximation of the problem by a mixed finite element method. We proveO(h) andO(h|lnh|1/2) error bounds respectively for the moments and the displacement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389591
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    Stability and accuracy for implicit semidiscretizations of hyperbolic problems (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 221-237 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    Approximation numérique du cisaillement transverse dans les plaques minces en flexion (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 281-302 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    On the construction of optimal mixed finite element methods for the linear elasticity problem (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 447-462 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    Stream vectors in three dimensional aerodynamics (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 561-589 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    On the multi-level splitting of finite element spaces (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 379-412 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    A remark on theL ∞ bounds of the Ritz operator associated with a finite element approximation (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 529-544 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    Analysis of the Kleiser-Schumann method (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 217-243 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Finite element solution of nonlinear elliptic problems (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 451-475 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    Estimates from above and from below for the homogenized coefficients (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 533-545 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS):65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The computation of the homogenized coefficients involves the solution of a minimum problem for a quadratic functional. The use of conforming finite elements provides estimates from above. In this paper we prove that, under realistic assumptions, the use of linear non-conforming finite elements provides estimates from below. Hence, a-posteriori error estimates for the homogenized coefficients can be obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408574
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    On the finite element approximation of a cascade flow problem (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 655-684 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    Electronic Resource
    Electronic Resource
    Optimal control of a Stefan problem with state-space constraints (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 723-744 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398381
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    Electronic Resource
    Electronic Resource
    A practical finite element approximation of a semi-definite Neumann problem on a curved domain (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 23-36 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper considers the finite element approximation of the semi-definite Neumann problem: −∇·(σ∇u)=f in a curved domain Ω⊂ℝ n (n=2 or 3), $$\sigma \frac{{\partial u}}{{\partial v}} = g$$ on πΩ and $$\int\limits_\Omega {u dx} = q$$ , a given constant, for dataf andg satisfying the compatibility condition $$\int\limits_\Omega {f dx} + \int\limits_{\partial \Omega } {g ds} = 0$$ . Due to perturbation of domain errors (Ω→Ω h ) the standard Galerkin approximation to the above problem may not have a solution. A remedy is to perturb the right hand side so that a discrete form of the compatibility condition holds. Using this approach we show that for a finite element space defined overD h , a union of elements, with approximation powerh k in theL 2 norm and with dist (Ω, Ω h )≦Ch k , one obtains optimal rates of convergence in theH 1 andL 2 norms whether Ω h is fitted (Ω h ≡D h ) or unfitted (Ω h ⊂D h ) provided the numerical integration scheme has sufficient accuracy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399693
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    Electronic Resource
    Electronic Resource
    Comparison of linear system solvers applied to diffusion-type finite element equations (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 529-546 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Various iterative methods for solving the linear systems associated with finite element approximations to self-adjoint elliptic differential operators are compared based on their performance on serial and parallel machines. The methods studied are all preconditioned conjugate gradient methods, differing only in the choice of preconditioner. The preconditioners considered arise from diagonal scaling, incomplete Cholesky decomposition, hierarchical basis functions, and a Neumann-Dirichlet domain decomposition technique. The hierarchical basis function idea is shown to be especially effective on both serial and parallel architectures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396343
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    Electronic Resource
    Electronic Resource
    Sur les éléments finis rationnels de Serendip de degré quelconque (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 175-187 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A general construction of rational finite elements of serendip type on convex quadrilaterals is described in this paper. A first technique consists in eliminating formerly introduced nodes; a second possibility is to use the transformation of Coxeter-Wachspress. Error bounds are given for the associate interpolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390418
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    W m,2 -Fehlerabschätzungen für Galerkin-Näherungen schwach elliptischer quasilinearer Randwertprobleme 2m-ter Ordnung (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 597-609 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65N15 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For weak elliptic quasilinear boundary value problems of order 2m inn dimensionsW m,2 -error estimates for the Galerkin method are established, in whichL ∞-norms of certain derivatives of the Galerkin approximations still occur. The order of these derivatives depends on several conditions on the coefficients of the differential operator. With the help of appropriate a priori bounds for the discrete solutions asymptotic error estimates for the finite element method may be obtained from this. This procedure yields quasioptimal results in several cases. Finally some examples are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389459
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    A nonconforming combined method for solving Laplace's boundary value problems with singularities (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 475-497 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389701
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    Numerical solutions for some coupled systems of nonlinear boundary value problems (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 381-394 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the well-known Volterra-Lotka model concerning two competing species with diffusion, the densities of the species are governed by a coupled system of reaction diffusion equations. The aim of this paper is to present an iterative scheme for the steady state solutions of a finite difference system which corresponds to the coupled nonlinear boundary value problems. This iterative scheme is based on the method of upper-lower solutions which leads to two monotone sequences from some uncoupled linear systems. It is shown that each of the two sequences converges to a nontrivial solution of the discrete equations. The model under consideration may have one, two or three nonzero solutions and each of these solutions can be computed by a suitable choice of initial iteration. Numerical results are given for these solutions under both the Dirichlet boundary condition and the mixed type boundary condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397542
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    A quadratic finite element method for solving biharmonic problems in ℝ n (1987)
    Springer
    Numerische Mathematik 52 (1987), S. 33-43 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A family of simplicial finite element methods having the simplest possible structure, is introduced to solve biharmonic problems in ℝ n ,n≧3, using the primal variable. The family is inspired in the MORLEY triangle for the two dimensional case, and in some sense this element can be viewed as its member corresponding to the valuen=2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401020
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    Approximation of a circular cylindrical shell by Clough-Johnson flat plate finite elements (1988)
    Springer
    Numerische Mathematik 52 (1988), S. 187-217 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 73K10 ; 73K15 ; 73K25 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we study the approximation of a right circular cylindrical shell by a nonconforming method using Clough-Johnson flat plate finite elements. Compatibility conditions which have to be satisfied by the degrees of freedom at every node of the triangulation are given. Then, we prove that convergence is insured for shallow shells when using particular families of triangulations which are practically easy to implement. Finally, we propose a new approximation method by flat plate finite elements which assures the convergence for any kind of circular cylindrical shell.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398689
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    Defect correction for nonlinear elliptic difference equations (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 199-208 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65B05 ; 65N20 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The present paper is concerned with the study of a high-order defect correction technique for discretizations of nonlinear elliptic boundary value problems. The convergence of the method is analyzed in general and, in more detail, for a specific example. The algorithmic combination of defect correction and multigrid techniques is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396749
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    A predictor-corrector technique for constrained least-squares regularization (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 353-367 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 47H10, 65M30, 65J15 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper describes a numerical strategy for the approximate solution of nonlinear, discretized, inverse problems by regularization. It is assumed that the solution of the associated direct problems and the computation of Fréchet derivatives are expensive. In order to minimize the amount of work, a predictor-corrector type algorithm is proposed. From a series of solutions to problems with a coarse discretization one obtains a starting approximation for a problem with a fine discretization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400119
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    Numerical methods for reaction-diffusion problems with non-differentiable kinetics (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 1-11 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS):65N30 ; 35J65 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395875
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    On the determination of higher order terms of singular elastic stress fields near corners (1988)
    Springer
    Numerische Mathematik 53 (1988), S. 51-95 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In two-dimensional elasticity stresses at reentrant corners exhibit singular behavior. The stress field is of the form $$\sigma = \Sigma {\rm K}_\iota r^{\lambda _2 - 1} f_i (\theta ;\lambda _i )$$ , where (r, θ) are polar coordinates centered at the tip of the corner, andf i (θ;λ i are smooth functions. For practical use of this series the eigenvaluesλ i (which are generally complex numbers) are required in order of ascending real part. The problem then is to find the roots of a transcendental equation (eigenequation) in the complex plane and arranged in order of ascending real part. A theorem is proved on the number, location and nature of the roots of this equation with the real part in fixed intervals of length π. Excellent initial estimates of the real part of the complex roots become available, and so are bounds, within which single real roots exist. This enables the determination of any number of roots in ascending order of real part. The critical angles at which the eigenvalues change nature are also determined. It is shown that for certain cases and for the symmetric mode of deformation, the eigenvalue λ=1 does not represent a rigid body rotation, therefore it has to be included in the series representation of the stresses. The coefficientsK i can be determined by recently developed extraction techniques, thus allowing complete determination of the elastic field and enabling its correlation with experimental data on brittle fracture, crack initiation, plastic zone estimation etc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395878
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    On the numerical solution of the equation $$\frac{{\partial ^2 z}}{{\partial x^2 }}\frac{{\partial ^2 z}}{{\partial y^2 }} - \left( {\frac{{\partial ^2 z}}{{\partial x\partial y}}} \right)^2 = f$$ and its discretizations, I (1989)
    Springer
    Numerische Mathematik 54 (1989), S. 271-293 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N05 ; 65G10 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The equation indicated in the title is the simplest representative of the class of nonlinear equations of Monge-Ampere type. Equations with such nonlinearities arise in dynamic meteorology, geometric optics, elasticity and differential geometry. In some special cases heuristic procedures for numerical solution are available, but in order for them to be successful a good initial guess is required. For a bounded convex domain, nonnegativef and Dirichlet data we consider a special discretization of the equation based on its geometric interpretation. For the discrete version of the problem we propose an iterative method that produces a monotonically convergent sequence. No special information about an initial guess is required, and to initiate the iterates a routine step is made. The method is self-correcting and is structurally suitable for a parallel computer. The computer program modules and several examples are presented in two appendices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396762
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    Convergence and comparison analysis of some numerical Schwarz methods (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 123-138 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N99 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Domain decomposition methods are a natural means for solving partial differential equations on multi-processors. The spatial domain of the equation is expressed as a collection of overlapping subdomains and the solution of an associated equation is solved on each of these subdomains. The global solution is then obtained by piecing together the subsolutions in some manner. For elliptic equations, the global solution is obtained by iterating on the subdomains in a fashion that resembles the classical Schwarz alternating method. In this paper, we examine the convergence behavior of different subdomain iteration procedures as well as different subdomain approximations. For elliptic equations, it is shown that certain iterative procedures are equivalent to block Gauss-Siedel and Jacobi methods. Using different subdomain approximations, an inner-outer iterative procedure is defined.M-matrix analysis yields a comparison of different inner-outer iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01409781
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    On some boundary element methods for the heat equation (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 101-120 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The object of this paper is to study some boundary element methods for the heat equation. Two approaches are considered. The first, based on the heat potential, has been studied numerically by previous authors. Here the convergence analysis in one space dimension is presented. In the second approach, the heat equation is first descretized in time and the resulting elliptic problem is put in the boundary formulation. A straight forward implicit method and Crank-Nicolson's method are thus studied. Again convergence in one space dimension is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400258
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    A three-dimensional quadratic nonconforming element (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 269-279 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We define a second-degree nonconforming element on tetrahedra. We build a basis for the opproximation space derived from this element. We prove a discrete regularity property similar to the one that holds for the corresponding two-dimensional element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390424
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    Monotone iterative methods for finite difference system of reaction-diffusion equations (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 571-586 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents an existence-comparison theorem and an iterative method for a nonlinear finite difference system which corresponds to a class of semilinear parabolic and elliptic boundary-value problems. The basic idea of the iterative method for the computation of numerical solutions is the monotone approach which involves the notion of upper and lower solutions and the construction of monotone sequences from a suitable linear discrete system. Using upper and lower solutions as two distinct initial iterations, two monotone sequences from a suitable linear system are constructed. It is shown that these two sequences converge monotonically from above and below, respectively, to a unique solution of the nonlinear discrete equations. This formulation leads to a well-posed problem for the nonlinear discrete system. Applications are given to several models arising from physical, chemical and biological systems. Numerical results are given to some of these models including a discussion on the rate of convergence of the monotone sequences.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389659
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    L 2 estimates for the finite element method for the Dirichlet problem with singular data (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 627-632 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider the approximation by the finite element method of second order elliptic problems on convex domains and homogeneous Dirichlet condition on the boundary. In these problems the data are Borel measures. Using a quasiuniform mesh of finite elements and polynomials of degree ≦1, we prove that in two dimensions the convergence is of orderh inL 2 and in three dimensions of orderh 1/2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389461
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    Superconvergence for a mixed finite elmenent method for elastic wave propagation in a plane domain (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 189-202 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    Multi-grid methods for Hamilton-Jacobi-Bellman equations (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 239-254 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    Numerical computation of least constants for the Sobolev inequality (1986)
    Springer
    Numerische Mathematik 48 (1986), S. 607-616 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Asymptotic error expansion and Richardson extranpolation for linear finite elements (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 11-37 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389427
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    Approximation of the solution of a fourth order boundary value problem with nonsmooth coefficient (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 125-145 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    Finite element approximation of the Dirichlet problem using the boundary penalty method (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 343-366 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    A new family of mixed finite elements in ℝ3 (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 57-81 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389668
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    Numerical solution of a hyperbolic free boundary problem with a method of characteristics (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 85-99 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N99 ; 35R35 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For a free boundary problem for a linear hyperbolic system in one space dimension with two unknowns we discuss a numerical algorithm which combines the method of characteristics and the front tracking method. We prove quadratic resp. linear convergence and illustrate this with numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400257
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    On finite element methods for the Neumann problem (1985)
    Springer
    Numerische Mathematik 46 (1985), S. 587-598 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Neumann problem for a second order elliptic equation with self-adjoint operator is considered, the unique solution of which is determined from projection onto unity. Two variational formulations of this problem are studied, which have a unique solution in the whole space. Discretization is done via the finite element method based on the Ritz process, and it is proved that the discrete solutions converge to one of the solutions of the continuous problem. Comparison of the two methods is done.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389660
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Alternating iteration and elliptic variational inequalities (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 459-481 
    Details
    ISSN: 0945-3245
    Keywords: MR 35A40 ; MR 39-04 ; MR 65N05 ; MR 65N20 ; MR 36S05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Free boundary value problems, too complicated for formulation as a variational inequality, are broken up into two problems on overlapping regions. On one region the problem is treated as an ordinary boundary value problem; on the second region, the “free boundary part” of the problem is reduced to a variational inequality. By solving the two problems successively it is shown that under certain conditions the successive solutions converge to a single function that gives a solution of the original problem. Application to a filtration problem is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389592
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    Finite difference approximations to the Dirichlet problem for elliptic systems (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 227-237 
    Details
    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→∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389626
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    An asymptotic finite element method for improvement of solutions of boundary layer problems (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 425-438 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389540
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    Analysis of a non-linear difference scheme in reaction-diffusion (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 511-527 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389703
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    A convergence analysis of hopscotch methods for fourth order parabolic equations (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 275-290 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389630
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Regions of stability, equivalence theorems and the Courant-Friedrichs-Lewy condition (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 319-329 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389633
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    Electronic Resource
    Electronic Resource
    Theh,p andh-p versions of the finite element method in 1 dimension (1986)
    Springer
    Numerische Mathematik 49 (1986), S. 577-612 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389733
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 45-55 
    Details
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    A conjugate gradient method and a multigrid algorithm for Morley s finite element approximation of the biharmonic equation (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 567-586 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The numerical solution of the linear equations arising from Morley's nonconforming displacement method is studied. A suitable preconditioning for the conjugate gradient method is described. Furthermore, the nonconformity of the discretization necessitates some non-standard ingredients of multigrid algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408577
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    Optimal L∞-error estimates for nonconforming and mixed finite element methods of lowest order (1987)
    Springer
    Numerische Mathematik 50 (1987), S. 587-611 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary For second order linear elliptic problems, it is proved that theP 1-nonconforming finite element method has the sameL ∞-asymptotic accuracy as theP 1-conforming one. This result is applied to derive optimalL ∞-error estimates for both the displacement and the stress fields of the lowest order Raviart-Thomas mixed finite element method, and a superconvergence result at the barycenter of each element.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408578
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...