## 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 ${\displaystyle [{H}_{0}^{1}(\Omega )]^{d}}$ and the pressure ${\displaystyle p\in {L}_{0}^{2}(\Omega )}$. First, we analyse standard DG methods assuming that the right-hand side f belongs to ${\displaystyle [H^{-1}(\Omega )\cap L^{1}(\Omega )]^{d}}$. A DG method that is well defined for f belonging to ${\displaystyle [H^{-1}(\Omega )]^{d}}$ 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.

### Document information

Published on 05/09/19

DOI: 10.1093/imanum/drt022