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  • Artikel  (27)
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  • 1
    Digitale Medien
    Digitale Medien
    Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 345-371 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01418330
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  • 2
    Digitale Medien
    Digitale Medien
    A convergence condition for the quadrilateral Wilson element (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 349-361 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405567
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5-17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: 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].
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01379662
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G18
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: 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.
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01389473
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  • 5
    Digitale Medien
    Digitale Medien
    Error analysis for Laplace transform —Finite element solution of hyperbolic equations (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 55-62 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396305
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  • 6
    Digitale Medien
    Digitale Medien
    An analysis of thep-version of the finite element method for nearly incompressible materials (1983)
    Springer
    Numerische Mathematik 41 (1983), S. 39-53 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; 73K25 CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper we analyze the behavior of the so-calledp-version of the finite element method when applied to the equations of plane strain linear elasticity. We establish optimal rate error estimates that are uniformly valid, independent of the value of the Poisson ratio,v, in the interval ]0, 1/2[. This shows that thep-versiondoes not exhibit the degeneracy phenomenon which has led to the use of various, only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396304
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  • 7
    Digitale Medien
    Digitale Medien
    On conforming finite element methods for the inhomogeneous stationary Navier-Stokes equations (1983)
    Springer
    Numerische Mathematik 42 (1983), S. 173-194 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01395310
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  • 8
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G.1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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|).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405570
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  • 9
    Digitale Medien
    Digitale Medien
    Approximation of tricomi problem with Neumann boundary condition (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 371-391 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N30 ; CR: G 1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405569
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  • 10
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65N30 ; CR: 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01390183
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