L∞-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities

Abstract

This paper deals with the finite element approximation of a class of variational inequalities (VI) and quasi-variational inequalities (QVI) with the right-hand side depending upon the solution. We prove that the approximation is optimally accurate in L∞ combining the Banach fixed point theorem with the standard uniform error estimates in linear VIs and QVIs. We also prove that this approach extends successfully to the corresponding noncoercive problems.