  In this article, a reliable and efficient a posteriori error estimator of
residual type is derived for a class of discontinuous Galerkin methods for the
frictional contact problem with reduced normal compliance which is modeled as a
quasi-variational inequality. We further derive a priori error estimates in the
energy norm under the minimal regularity assumption on the exact solution. The
convergence behavior of error over uniform mesh and the performance of error
estimator are illustrated by the numerical results.
