On a direct approach to adaptive FE-discretisations for elliptic variational inequalities

Abstract

The techniques to derive residual based error estimators for finite element discretisations of variational equations can be extended directly to variational inequalities by employing a suitable adaptation of Nitsche's idea (c.f. [8]). This strategy is presented here for elliptic variational inequalities. Its application is demonstrated at the obstacle problem, where numerical results show that the proposed approach to a posteriori error control gives useful error bounds.