Error estimates for the approximation of a class of variational inequalities

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 = \{ H₀¹ (): a. e. in Ω.