Error estimates for the approximation of a class of variational inequalities

Abstract:

In this paper, we prove a general approximation theorem useful in obtaining order of convergence estimates for the approximation of the solutions of a class of variational inequalities. The theorem is then applied to obtain an "optimal" rate of convergence for the approximation of a second-order elliptic problem with convex set $K = \{ \upsilon \in H_0^1(\Omega ):\upsilon \geqslant \chi$ a.e. in $\Omega$}.