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| − | 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 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. | + | 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. |
Revision as of 13:22, 5 September 2019
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 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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