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hp ‐Adaptive Finite Element Methods for Variational Inequalities
Author(s) -
Schröder Andreas
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810053
Subject(s) - a priori and a posteriori , variational inequality , polygon mesh , finite element method , saddle point , mathematics , convergence (economics) , mathematical optimization , obstacle problem , exponential function , mathematical analysis , geometry , engineering , philosophy , structural engineering , epistemology , economics , economic growth
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 yposteriori 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)