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  • Articles  (595)
  • Mathematics and Statistics  (520)
  • 65N30  (75)
  • 1990-1994  (595)
  • Mathematics  (595)
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  • Articles  (595)
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  • 1
    Electronic Resource
    Electronic Resource
    Fourier-Chebyshev pseudospectral method for two-dimensional vorticity equation (1993)
    Springer
    Numerische Mathematik 66 (1993), S. 329-346 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 76D99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Fourier-Chebyshev pseudospectral scheme is proposed for two-dimensional unsteady vorticity equation. The generalized stability and convergence are proved strictly. The numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385701
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  • 2
    Electronic Resource
    Electronic Resource
    Finite element analysis of a holonomic elastic-plastic problem (1991)
    Springer
    Numerische Mathematik 60 (1991), S. 493-508 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A thorough analysis of the finite element method is given for a holonomic elastic-plastic problem. An inequality of the Cea's lemma type is proved, which is the basis of error estimates for various finite element solutions. Difficulty caused by a non-differentiable term in the problem can be overcome by using two convergent procedures, an iterative procedure and a regularization procedure. An a-posteriori quantitative error estimate is derived for the regularized solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385733
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  • 3
    Electronic Resource
    Electronic Resource
    The hierarchical basis multigrid method for convection-diffusion equations (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 7-37 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We make a theoretical study of the application of a standard hierarchical basis multigrid iteration to the convection diffusion equation, discretized using an upwind finite element discretizations. We show behavior that in some respects is similar to the symmetric positive definite case, but in other respects is markedly different. In particular, we find the rate of convergence depends significantly on parameters which measure the strength of the upwinding, and the size of the convection term. Numerical calculations illustrating some of these effects are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385495
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  • 4
    Electronic Resource
    Electronic Resource
    Arch beam models: finite element analysis and superconvergence (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 117-143 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper studies finite element methods for a class of arch beam models. For both standard and mixed methods, existence and uniqueness results are proved, optimal rates of convergence are obtained and the superconvergence property is established. Reduced integration is shown to be an efficient method for arch beam problems and selected reduced integration is found to be identical to the mixed method. The significance of the analysis is threefold. The mixed method and the reduced integration methods converge uniformly at the optimal rate with respect to the arch thickness parameter, so they are locking free. Second, mixed method and reduced integration keep the superconvergence properties of the standard method. Finally, this is the first attempt to investigate the superconvergence of finite element methods for arch beam problems. We set up two types of superconvergence results: displacement at the nodal points and gradient at the Gauss points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385501
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  • 5
    Electronic Resource
    Electronic Resource
    Convergence rate estimate for a domain decomposition method (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 153-169 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385503
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  • 6
    Electronic Resource
    Electronic Resource
    Streamline diffusion finite element method for quasilinear elliptic problems (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 335-357 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We extend the analysis of the streamline diffusion finite element method to quasilinear elliptic problems of second order. An existence theorem and error estimates are given in the case of branches of nonsingular solutions following a recent abstract approach in [12, 13, 26].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385513
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  • 7
    Electronic Resource
    Electronic Resource
    The problem of membrane locking in finite element analysis of cylindrical shells (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 523-542 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 73C20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We analyse the problem of membrane locking in (h, p) finite element models of a thin hemicylindrical shell roof loaded by a smoothly varying normal pressure distribution. We show that in the standard finite element method, locking occurs especially at low values ofp and when the finite element grid is not aligned with the axis of the cylinder. A general strategy of avoiding locking by using modified bilinear forms is introduced, and a special implementation of this strategy on aligned rectangular grids is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385524
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  • 8
    Electronic Resource
    Electronic Resource
    Boundary Lagrange multipliers in finite element methods: Error analysis in natural norms (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 1-15 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A finite element procedure for circumventing the Babuška-Brezzi condition in mixed formulations with Lagrange multipliers defined on the boundary is presented. Residual terms constructed from the Euler-Lagrange equations are added to the classical Galerkin formulation in order to attain coercivity in a mesh-dependent norm. Convergence is proven for the primal variable and the multiplier in the natural mesh-independent norm of the problem, generalizing results of a previous paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396217
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  • 9
    Electronic Resource
    Electronic Resource
    Analyse d'un élément mixte pour le problème de Stokes (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 161-188 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Résumé Nous construisons un élément fini mixte pour le problème de Stokes. Cet élément est non conforme. Nous appliquons les résultats de la Partie I pour obtenir des estimations d'erreur optimales. Nous considérons aussi le traitement des conditions de raccords par des multiplicateurs de Lagrange et nous montrons que ces multiplicateurs peuvent être utilisés pour construire une approximation superconvergente.
    Notes: Summary We build a mixed finite element method for the Stokes problem. This method is nonconforming. We apply the results of Part I to prove convergence and obtain optimal error estimates. We also consider the treatment of interface conditions by multipliers and show that a superconvergent approximation can be built from those multipliers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396225
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  • 10
    Electronic Resource
    Electronic Resource
    On a hierarchical basis multilevel method with nonconforming P1 elements (1992)
    Springer
    Numerische Mathematik 62 (1992), S. 189-212 
    Details
    ISSN: 0945-3245
    Keywords: 65F10 ; 65F35 ; 65N20 ; 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We develop a hierarchical basis multilevel method for symmetric second order elliptic boundary value problems in two-dimensional polygonal domains based on nonconforming P1 triangular elements. The main result is that the condition number of the hierarchical discretization is bounded byO(k) wherek is the number of refinement levels. For comparison, Yserentant's result yields the sharp boundO(k 2) for the corresponding hierarchical discretization with conforming linear elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396226
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