Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity

Abstract

In this article, we analyze several discontinuous Galerkin methods (DG) for the Stokes problem under the minimal regularity on the solution. We assume that the velocity u belongs to [H1 0 (­)]d and the pressure p 2 L2 0 (­). First, we analyze standard DG methods assuming that the right hand side f belongs to [H¡1(­) \ L1(­)]d. A DG method that is well de¯ned for f belonging to [H¡1(­)]d is then investigated. The methods under study include stabilized DG methods using equal order spaces and inf-sup stable ones where the pressure space is one polynomial degree less than the velocity space.