Repository: Freie Universit├Ąt Berlin, Math Department

Monotone methods on non-matching grids for non-linear contact problems

Wohlmuth, B. and Krause, R. (2003) Monotone methods on non-matching grids for non-linear contact problems. SIAM J. Sci. Comput., 25 (1). pp. 324-347. ISSN 1064-8275

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Official URL: https://dx.doi.org/10.1137/S1064827502405318

Abstract

Nonconforming domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We use a generalized mortar method based on dual Lagrange multipliers for the discretization of a nonlinear contact problem between linear elastic bodies. In the case of unilateral contact problems, pointwise constraints occur and monotone multigrid methods yield efficient iterative solvers. Here, we generalize these techniques to nonmatching triangulations, where the constraints are realized in terms of weak integral conditions. The basic new idea is the construction of a nested sequence of nonconforming constrained spaces. We use suitable basis transformations and a multiplicative correction. In contrast to other approaches, no outer iteration scheme is required. The resulting monotone method is of optimal complexity and can be implemented as a multigrid method. Numerical results illustrate the performance of our approach in two and three dimensions.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1836
Deposited By: Ekaterina Engel
Deposited On:15 Apr 2016 12:31
Last Modified:03 Mar 2017 14:42

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