A posteriori error estimation and adaptive solution of elliptic variational inequalities of the second kind

Authors:
Viorel Bostan;Weimin Han;B. D. Reddy
Affiliations:
Department of Mathematics, University of Iowa, Iowa City, IA;Department of Mathematics, University of Iowa, Iowa City, IA;Department of Mathematics and Applied Mathematics, University of Cape Town, 7700 Rondebosch, South Africa
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

In this paper, we perform an a posteriori error analysis for adaptive finite element solutions of elliptic variational inequalities of the second kind. A general framework for a posteriori error estimates is established by using duality theory in convex analysis. We then turn to an analysis of some particular a posteriori error estimates of residual type. Efficiency of the error estimators are investigated. Numerous numerical examples are included to illustrate the effectiveness of the a posteriori error estimates in adaptive solutions of the variational inequalities.