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 = { υ ∈ H 0 1 ( Ω ) : υ ⩾ χ K = \{ \upsilon \in H_0^1(\Omega ):\upsilon \geqslant \chi a.e. in Ω \Omega }.