Unified analysis of discontinuous Galerkin methods for frictional contact problem with normal compliance

Abstract

The main contributions of this article are twofold. Firstly, we develop a reliable and efficient a posteriori error estimator for a class of discontinuous Galerkin methods for the frictional contact problem with reduced normal compliance (which is modeled as a quasi-variational inequality). Secondly, we establish medius analysis (a priori error analysis under the minimal regularity assumption on the exact solution) in the energy norm for the underlying problem. Numerical results substantiate the convergence behavior of the error over uniform mesh and performance of a posteriori error estimator over adaptive mesh.