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  • 1995-1999  (5)
  • 1985-1989  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Monotone multigrid methods for elliptic variational inequalities II (1996)
    Springer
    Numerische Mathematik 72 (1996), S. 481-499 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65N30, 65N55, 35J85
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements. The coarse grid corrections are computed from certain obstacle problems. The actual constraints are fixed by the preceding nonlinear fine grid smoothing. This new approach allows the implementation as a classical V-cycle and preserves the usual multigrid efficiency. We give $1-O(j^{-3})$ estimates for the asymptotic convergence rates. The numerical results indicate a significant improvement as compared with previous multigrid approaches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050178
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    Paper (German National Licenses)
    Fulltext
  • 2
    Book
    Book
    Adaptive monotone multigrid methods for nonlinear variational problems (1997)
    Stuttgart :Teubner,
    Details
    Title: Adaptive monotone multigrid methods for nonlinear variational problems
    Author: Kornhuber, Ralf
    Publisher: Stuttgart :Teubner,
    Year of publication: 1997
    Pages: 157 S.
    Series Statement: Advances in Numerical Mathematics
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 3
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    Unknown
    Multi-Grid Solution of Two Coupled Stefan Equations Arising in Induction Heating of Large Steel Slabs. (1988)
    Details
    Publication Date: 2014-02-26
    Description: Induction heating of large steel slabs can be described by a coupled system of nonlinear evolution equations of Stefan type representing the temporal and spatial distribution of the induced magnetic field and the generated temperature within the slab. Discretizing these equations implicitly in time and by finite differences in space, at each time step the solution of a system of difference inclusions is required. For the solution of that system two multi-grid algorithms are given which combined with a nested iteration type continuation strategy to proceed in time result in computationally highly efficient schemes for the numerical simulation of the induction heating process. {\bf Keywords:} induction heating, system of two coupled Stefan equations, multi-grid algorithms. {\bf Subject Classification:} AMS(MOS): 35K60, 35R35, 65H10, 65N05, 65N20, 78A25, 78A55.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 4
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    Monotone Iterations for Elliptic Variational Inequalities (1998)
    Details
    Publication Date: 2014-02-26
    Description: A wide range of free boundary problems occurring in engineering andindustry can be rewritten as a minimization problem for astrictly convex, piecewise smooth but non--differentiable energy functional.The fast solution of related discretized problemsis a very delicate question, because usual Newton techniquescannot be applied. We propose a new approach based on convex minimization and constrained Newton type linearization. While convex minimization provides global convergence of the overall iteration, the subsequent constrained Newton type linearization is intended to accelerate the convergence speed. We present a general convergence theory and discuss several applications.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 5
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    On Robust Multigrid Methods for Piecewise Smooth Variational Problems (1996)
    Details
    Publication Date: 2014-02-26
    Description: We consider the fast solution of large, piecewise smooth minimization problems as resulting from the approximation of elliptic free boundary problems. The most delicate question in constructing a multigrid method for a nonlinear, non--smooth problem is how to represent the nonlinearity on the coarse grids. This process usually involves some kind of linearization. The basic idea of monotone multigrid methods to be presented here is first to select a neighborhood of the actual smoothed iterate in which a linearization is possible and then to constrain the coarse grid correction to this neighborhood. Such a local linearization allows to control the local corrections at each coarse grid node in such a way that the energy functional is monotonically decreasing. This approach leads to globally convergent schemes which are robust with respect to local singularities of the given problem. The numerical performance is illustrated by approximating the well-known Barenblatt solution of the porous medium equation.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
  • 6
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    Adaptive Finite-Elemet- Methoden für konvektionsdominierte Randwertprobleme bei partiellen Differentialgleichungen. (1989)
    Details
    Publication Date: 2014-02-26
    Description: Ausgangspunkt bei der Behandlung konvektiv dominierter, elliptischer Probleme sind die bekannten hierarchischen Finite-Element-Methoden für den rein elliptischen Fall. Als stabile Erweiterung des Standard-Galerkin-Verfahrens wird das Stromlinien-Diffusions-Verfahren durch physikalische Überlegungen motiviert und kurz diskutiert. Anschließend zeigen wir, daß diese Methode erst in Verbindung mit einer hier erstmals vorgestellten lokalen Ausrichtung der Kanten wirksam eingesetzt werden kann. Zusammen mit einer ebenfalls neu entwickelten richtungsorientierten Verfeinerungsstrategie erhält man eine erheblich stabilere, genauere und schnellere Auflösung von Grenzschichten als mit herkömmlichen Methoden.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 7
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    On Adaptive Grid Refinement in the Presence of Internal or Boundary Layers. (1989)
    Details
    Publication Date: 2014-02-26
    Description: We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resolution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. It is demonstrated by several numerical examples that compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. {\bf Keywords:} Adaptive finite elements, directed refinement, adaptive grid orientation, convection diffusion equation, internal and boundary layers.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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    OPUS
  • 8
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    Globally Convergent Multigrid Methods for Porous Medium Type Problems (1997)
    Details
    Publication Date: 2014-02-26
    Description: We consider the fast solution of large, piecewise smooth minimization problems as typically arising from the finite element discretization of porous media flow. For lack of smoothness, usual Newton multigrid methods cannot be applied. We propose a new approach based on a combination of convex minization with {\em constrained} Newton linearization. No regularization is involved. We show global convergence of the resulting monotone multigrid methods and give logarithmic upper bounds for the asymptotic convergence rates.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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    OPUS
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