A Posteriori Error Estimation in Mixed Finite Element Methods for Signorini’s Problem

Abstract

This paper presents a posteriori error estimates for Signorini's problem which is discretized via a mixed finite element approach. The error control relies on the estimation of the discretization error of an auxiliary problem given as a varia-tional equation. The resulting error estimates capture the discretization error of the auxiliary problem, the geometrical error and the error given by the complementary condition. The estimates are applied within adaptive finite element schemes. Nu-merical results confirm the applicability of the theoretical findings.