Adaptive discontinuous Galerkin methods for solving an incompressible Stokes flow problem with slip boundary condition of frictional type

We consider the numerical solution of a variational inequality arising in the study of an incompressible Stokes flow with a nonlinear slip boundary condition of frictional type. We study several discontinuous Galerkin (DG) schemes for solving the problem, and derive reliable and efficient residual type a posteriori error estimators. An adaptive DG method is constructed based on the error estimators to solve the problem. Some numerical examples are presented to illustrate the efficiency of the adaptive DG method.