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

Abstract

This work is concerned with the discontinuous Galerkin nite approximations 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 regular boundary, we formulate the problem and its discontinuous Galerkin approximations as mixed variational inequalities of the second kind with primitive variables. The well posedness of the formulated problems are established by means of a generalization of the Babuska-Brezzi theory for mixed problems. Finally, a priori error estimates using energy norm for both the velocity and pressure are obtained.

Keywords: Stokes equations, slip boundary condition, variational inequality, discontinuous Galerkin method, a priori error estimate, convergence

Quaestiones Mathematicae 36(2013), 501-516