Discontinuous Galerkin methods for solving a quasistatic contact problem

We consider the numerical solution of a nonlinear evolutionary variational inequality, arising in the study of quasistatic contact problems. We study spatially semi-discrete and fully discrete schemes for the problem with several discontinuous Galerkin discretizations in space and finite difference discretization in time. Under appropriate regularity assumptions on the solution, a unified error analysis is established for the schemes, reaching the optimal convergence order for linear elements. Numerical results are presented on a two dimensional test problem to illustrate numerical convergence orders.