Discontinuous Galerkin finite element discretization for steady stokes flows with threshold slip boundary condition

摘要

This work is concerned with the discontinuous Galerkin nite approxima-tions for the steady Stokes equations driven by slip boundary condition of \friction"type. Assuming that the ow region is a bounded, convex domain with a regularboundary, we formulate the problem and its discontinuous Galerkin approximationsas mixed variational inequalities of the second kind with primitive variables. The wellposedness of the formulated problems are established by means of a generalizationof the Babu ska-Brezzi theory for mixed problems. Finally, a priori error estimatesusing energy norm for both the velocity and pressure are obtained.