Discontinuous Galerkin methods for a contact problem with Tresca friction arising in linear elasticity

In this article, we propose and analyze discontinuous Galerkin (DG) methods for a contact problem with Tresca friction for the linearized elastic material. We derive a residual based a posteriori error estimator for the proposed class of DG methods. The reliability and the efficiency of a posteriori error estimator is shown. We further investigate a priori error estimates under the minimal regularity assumption on the exact solution. An important property shared by a class of DG methods, allow us to carry out the analysis in a unified framework. Numerical experiments are reported to illustrate theoretical results.