Discontinuous Galerkin Methods for Hemivariational Inequalities in Contact Mechanics

In this paper, we study discontinuous Galerkin (DG) methods for solving two contact problems. The first problem involves a frictionless normal compliance contact boundary condition, and the second is a bilateral contact problem with friction. These contact problems are modeled by hemivariational inequalities, which consist of non-convex and non-smooth terms. We apply five DG methods to solve the contact problems and establish a priori error estimates for these methods. We prove that the DG schemes achieve optimal convergence order for linear elements. Two examples are presented for numerical evidence of the theoretically predicted convergence order.