Error analysis of discontinuous Galerkin methods for the Stokes problem under minimum regularity

== Abstract ==

In this article, we analyse several discontinuous Galerkin (DG) methods for the Stokes problem under minimal regularity on the solution. We assume that the velocity u belongs to <math>[{H}^1_0(\Omega)]^d</math> and the pressure <math>p\in {L}^2_0(\Omega)</math>. First, we analyse standard DG methods assuming that the right-hand side f belongs to <math>[H^{-1}(\Omega)\cap L^1(\Omega)]^d</math>. A DG method that is well defined for f belonging to <math>[H^{-1}(\Omega)]^d</math> 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.