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  • Articles  (10)
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  • Articles  (10)
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  • Springer  (10)
  • American Meteorological Society
  • American Physical Society (APS)
  • Blackwell Publishing Ltd
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  • 1
    Electronic Resource
    Electronic Resource
    A convergence condition for the quadrilateral Wilson element (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 349-361 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper deals with the convergence properties of the nonconforming quadrilateral wilson element which violates the patch test. The convergence of the element is proved under a certain condition on mesh subdivisions without any modifications of the variational formulation. This result extends the range of applicability of Wilson's element. The necessity of the proposed condition is also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405567
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  • 2
    Electronic Resource
    Electronic Resource
    Approximation de quelques problèmes de type Stokes par une méthode d'éléments finis mixtes (1984)
    Springer
    Numerische Mathematik 45 (1984), S. 75-91 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5-17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary We present in this paper a mixed-finite element approximation of Stokes equations with boundary conditions of Fourier's or Neumann's type. For this approximation we prove that the error estimates for the velocity-vector and for the pressure are optimal. These results of convergence generalize to this kind of boundary conditions the Glowinski-Pironneau's approximation of Stokes problem with Dirichlet's boundary conditions [9, 10].
    Notes: Résumé Nous présentons dans cet article une méthode d'éléments finis mixtes qui permet la résolution des équations de Stokes avec des conditions aux limites de type Fourier ou Neumann. Pour cette méthode nous démontrons que les estimations de l'erreur d'approximation sont optimales; en vitesse et en pression. Ces résultats de convergences généralisent à ce type non standard de conditions aux limites les travaux de Glowinski-Pironneau [9, 10] pour le probleme de Stokes avec des conditions aux limites de Dirichlet.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01379662
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  • 3
    Electronic Resource
    Electronic Resource
    Estimations des erreurs de meilleure approximation polynomiale et d'interpolation de Lagrange dans les espaces de Sobolev d'ordre non entier (1984)
    Springer
    Numerische Mathematik 45 (1984), S. 301-321 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary Explicit bounds for the best polynomial approximation error, explicit and non-explicit bounds for the Lagrange interpolation error are derived for functions belonging to fractional order Sobolev spaces defined over a bounded open set in ℝ n . Thus the classical results of the integer order Sobolev spaces are extended.
    Notes: Résumé On établit des majorations explicites de I'erreur de meilleure approximation polynomiale ainsi que des majorations explicites et nonexplicites de I'erreur d'interpolation de Lagrange, lorsque la fonction considérée appartient à un espace de Sobolev d'ordre non entier défini sur un ouvert borné de ℝ n . Les résultats obtenus généralisent les résultats connus dans le cas des espaces de Sobolev d'ordre entier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389473
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  • 4
    Electronic Resource
    Electronic Resource
    Eine Aussage zurL ∞-Stabilität und zur genauen Konvergenzordnung derH 0 1 -Projektionen (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 393-405 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G.1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we settle a question concerning the necessity of the logh-factor appearing in error estimates of linear finite element solutions. Let Ω⊂ℝ2 be a bounded convex polygon and {T h } a regular family of subdivisions of Ω into triangles. Be furtherS 0 h ⊂H 0 1 (Ω) the corresponding linear finite element spaces andP h :H 0 1 (Ω)→S 0 h theH 0 1 -projections. With respect to the uniform norm asymptotically estimates of the form $$\parallel u - P_h u\parallel _\infty \leqq c|logh|dist(u,S_0^h ), u \in C(\bar \Omega ) \cap H_0^1 (\Omega )$$ hold, as pointed out by Schatz [1980]. For functionsu with bounded second derivatives this implies $$\parallel u - P_h u\parallel _\infty \leqq ch^2 |\log h||u|_{2,\infty } ,$$ a result which was proved by Nitsche [1975] and Scott [1976] with different methods. It was an open question if the factor |logh| is necessary or only due to the methods of proof. In this paper it is shown by an example that the cited estimates are sharp in the very strong sense that in general they are no longer valid if |logh| is replaced by a termo(|logh|).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405570
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  • 5
    Electronic Resource
    Electronic Resource
    Approximation of tricomi problem with Neumann boundary condition (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 371-391 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G 1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The Tricomi problem with Neumann boundary condition is reduced to a degenerate problem in the elliptic region with a non-local boundary condition and to a Cauchy problem in the hyperbolic region. A variational formulation is given to the elliptic problem and a finite element approximation is studied. Also some regularity results in weighted Sobolev spaces are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405569
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  • 6
    Electronic Resource
    Electronic Resource
    Monotone explicit iterations of the finite element approximations for the nonlinear boundary value problem (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 419-437 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem Δu=bu 2, based on piecewise linear polynomials and the lumping operator. These iterations construct the monotonically decreasing and increasing sequences, and convergence proofs are given. Finally, we present some numerical examples verifying the effectiveness of the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390183
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  • 7
    Electronic Resource
    Electronic Resource
    Free boundary problems with nonlinear source terms (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 463-483 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The method of lines is used to semi-discretize the non-linear Poisson equation over a domain with a free boundary. The resulting multipoint free boundary problem is solved with a line Gauss-Seidel method which is shown to converge monotonically. The method of lines solution is then shown to converge to the continuous solution of the variational inequality form of the obstacle problem. Some numerical results for the diffusion-reaction equation indicate that the method is applicable to more general free boundary problems for nonlinear elliptic equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390185
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  • 8
    Electronic Resource
    Electronic Resource
    Combined finite element and spectral approximation of the Navier-Stokes equations (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 201-217 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Resumé On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.
    Notes: Summary We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410105
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  • 9
    Electronic Resource
    Electronic Resource
    On the stability of bilinear-constant velocity-pressure finite elements (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 219-222 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An analysis of the Babuška stability of bilinear/constant finite element pairs for viscous flow calculations is given. An unstable mode not of the checkerboard type is given for which the stability constant turns out to beO(h). Thus, the indicated spaces are not stable in general for numerical calculation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410106
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  • 10
    Electronic Resource
    Electronic Resource
    On numerical asymptotic behavior of finite element solutions for parabolic equations (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 285-300 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we investigate the numerical asymptotic behavior of the finite element solutions for linear parabolic equations under some appropriate conditions. We also give some results of numerical experiments in the two dimensional problems to indicate the effectiveness of our results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01410112
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