Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity
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 b...
| Authors: | ; ; ; |
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| Format: | Report |
| Publication date: | 2012 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/16922 |
| Online Access: | https://hdl.handle.net/2117/16922 |
| Access Level: | Open access |
| Keyword: | Galerkin methods Navier-Stokes equations Equacions de Navier-Stokes Metode Galerkin discontinu Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits |
| Summary: | 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. |
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