Preprint No. A-99-09

Ralf Kornhuber, Rolf Krause

On Monotone Multigrid Methods for the Signorini Problem

Abstract: We present a new approach for solving the Signorini problem in linear elasticity. The Signorini Problem is deemed to be the prototype of contact problems and describes the linearized contact of an linearly elastic body with a rigid foundation. Because it is not known in advance which part of the body's surface will come into contact with the foundation, the corresponding energy functional to be minimized is piecewise smooth but not differentiable on the contact boundary. Using monotone multigrid methods this nonlinear and nondifferentiable problem can be solved without any regularisation or Lagrangian multipliers.

Keywords: multigrid methods, elasticity, finite elements

Mathematics Subject Classification (MSC91): 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods , 65N55 Multigrid methods; domain decomposition

Language: ENG

Available:Pr-A-99-09.ps

Contact: Kornhuber, Ralf; Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (kornhube@math.fu-berlin.de)

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