\(L^\infty\)-error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities (Q5957223)

Summary: 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 \(L^\infty\) 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.