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 |
| _version_ | 1878736192410746881 |
|---|---|
| author | Badia, Santiago|||0000-0003-2391-4086 |
| author2 | Codina, Ramon|||0000-0002-7412-778X Gudi, Thirupathi Guzmán, Johnny |
| author2_role | author author author |
| author_browse | Badia, Santiago|||0000-0003-2391-4086 Codina, Ramon|||0000-0002-7412-778X Gudi, Thirupathi Guzmán, Johnny |
| author_facet | Badia, Santiago|||0000-0003-2391-4086 Codina, Ramon|||0000-0002-7412-778X Gudi, Thirupathi Guzmán, Johnny |
| author_role | author |
| collection | UPCommons. Portal del coneixement obert de la UPC |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | report |
| id | ES_8aa764c8aebd4e1f60c0a95fa59ac462 |
| institution | Universitat Politècnica de Catalunya (UPC) |
| instname_str | Universitat Politècnica de Catalunya (UPC) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:upcommons.upc.edu:2117/16922 |
| publishDate | 2012 |
| publishDateSort | 2012 |
| reponame_str | UPCommons. Portal del coneixement obert de la UPC |
| spelling | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity Badia, Santiago|||0000-0003-2391-4086 Codina, Ramon|||0000-0002-7412-778X Gudi, Thirupathi Guzmán, Johnny 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 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. https://hdl.handle.net/2117/16922 |
| spellingShingle | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity Badia, Santiago|||0000-0003-2391-4086 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 |
| title | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| title_full | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| title_fullStr | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| title_full_unstemmed | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| title_short | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| title_sort | Error analysis of discontinuous Galerkin methods for Stokes problem under minimal regularity |
| topic | 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 |
| topic_facet | 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 |
| url | https://hdl.handle.net/2117/16922 |