Reliable and Efficient a Posteriori Error Estimates of DG Methods for a Simplified Frictional Contact Problem

Abstract

A posteriori error estimators are studied for discontinuous Galerkin methods for solving a representative elliptic variational inequality of the second kind, known as a simplified frictional contact problem. The estimators are derived by relating the error of the variational inequality to that of a linear problem. Reliability and efficiency of the estimators are theoretically proved.