Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity
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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.
CitationBadia, S. [et al.]. "Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity". 2012.