A fixed-point approximation method for some noncoercive variational problems

Abstract

This paper deals with the finite-element approximation of some variational problems, namely, linear elliptic boundary value problems, variational inequalities, and quasi-variational inequalities with noncoercive operators. To prove optimal L ∞-error estimates, we introduce a simple and direct argument combining continuous piecewise linear finite elements with the Banach fixedpoint theorem