Discontinuous Galerkin Finite Element Method for a Nonlinear Boundary Value Problem

In this paper,we investigate the a priori and a posteriori error estimates for the discontinuous Galerkin finite element approximation to a regularization version of the variational inequality of the second kind.We show the optimal error estimates in the DG-norm(stronger than the H1norm)and the L2norm,respectively.Furthermore,some residual-based a posteriori error estimators are established which provide global upper bounds and local lower bounds on the discretization error.These a posteriori analysis results can be applied to develop the adaptive DG methods.