Adaptive Finite Element Methods for Variational Inequalities.

Andreas Schroeder

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 08-10, 4

MSC 2000

65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract
In this work, we combine an hp-adaptive strategy with a posteriori error estimates for variational inequalities, which are given by contact problems. The a posteriori error estimates are obtained using a general approach based on the saddle point formulation of contact problems and making use of a posteriori error estimates for variational equations. Error estimates are presented for obstacle problems and Signorini problems with friction. Numerical experiments confirm the reliability of the error estimates for finite elements of higher order. The use of the hp-adaptive strategy leads to meshes with the same characteristics as geometric meshes and to exponential convergence.