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 and the pressure . First, we analyse standard DG methods assuming that the right-hand side f belongs to . A DG method that is well defined for f belonging to 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.

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Published on 05/09/19

DOI: 10.1093/imanum/drt022
Licence: CC BY-NC-SA license

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