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

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.