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  • Articles  (27)
  • AMS(MOS): 65N30  (10)
  • CR: 5.15  (9)
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  • Springer  (27)
  • American Meteorological Society
  • American Physical Society (APS)
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  • International Union of Crystallography
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  • Mathematics  (27)
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  • Articles  (27)
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  • Springer  (27)
  • American Meteorological Society
  • American Physical Society (APS)
  • Blackwell Publishing Ltd
  • Cambridge University Press
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  • 1995-1999
  • 1980-1984  (27)
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  • 1
    Electronic Resource
    Electronic Resource
    A method of solving nonlinear variational problems by nonlinear transformation of the objective functional. Part I (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 59-82 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65K10 ; CR: 5.15 ; 5.41
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A general globally convergent iterative method for solving nonlinear variational problems is introduced. The method is applied to a temperature control problem and to the minimal surface problem. Several aspects of finite element implementation of the method are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389638
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  • 2
    Electronic Resource
    Electronic Resource
    Das modifizierte Newton-Verfahren in verallgemeinerten Banach-Räumen (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 91-104 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65J15 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A Newton-Kantorowitsch-analysis of the modified Newton's method in generalized Banach-spaces is given. The application of generalized norms — mappings from a linear space into an ordered Banach-space — improves convergence- and existence results as well as error estimates compared with the real-norm theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389640
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  • 3
    Electronic Resource
    Electronic Resource
    A general convergence theorem for the reduced gradient method (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 241-247 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 90C30 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Consider the problem of minimizing a real function subject to linear equality constraints and to nonnegativity bounds on the variables. A convergence theorem is established for a general algorithm model based on the reduced gradient method. The most meaningful assumptions that are made, concern two crucial points: the choice of the independent variables and that of the search direction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390125
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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Algorithmes mixtes asynchrones. Etude de convergence monotone (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 363-369 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In this paper we introduce two classes of iterative algorithms which we call “Asynchronous mixed algorithms” and we study their convergence under partial ordering. These algorithms can be implemented just as well on monoprocessors as on multiprocessors, and, along with their convergence study, constitute a generalization of the mixed classical “Newton-relaxation” algorithms.
    Notes: Résumé Nous introduisons dans cet article deux classes d'algorithmes itératifs que nous appelons «Algorithmes mixtes asynchrones» et nous en étudierons la convergence selon un ordre partiel. Ces algorithmes sont implémentables aussi bien sur les monoprocesseurs que sur les multiprocesseurs, et avec leur étude de convergence constituent une généralisation des algorithmes mixtes classiques «Newton-relaxation».
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405568
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  • 8
    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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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    A quadratic approximation method for minimizing a class of quasidifferentiable functions (1984)
    Springer
    Numerische Mathematik 45 (1984), S. 411-430 
    Details
    ISSN: 0945-3245
    Keywords: AMS MOS ; 90C30 ; 65K05 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An unconstrained nonlinear programming problem with nondifferentiabilities is considered. The nondifferentiabilities arise from terms of the form max [f 1(x), ...,f n (x)], which may enter nonlinearly in the objective function. Local convex polyhedral upper approximations to the objective function are introduced. These approximations are used in an iterative method for solving the problem. The algorithm proceeds by solving quadratic programming subproblems to generate search directions. Approximate line searches ensure global convergence of the method to stationary points. The algorithm is conceptually simple and easy to implement. It generalizes efficient variable metric methods for minimax calculations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01391417
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