Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem
A modified Chorin–Teman (Euler non-incremental) projection method and a modified Euler incremental projection method for non inf-sup stable mixed finite elements are analyzed. The analysis of the classical Euler non-incremental and Euler incremental methods are obtained as a particular case. We firs...
| Autores: | ; ; |
|---|---|
| Tipo de documento: | Artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/684669 |
| Acceso en línea: | http://hdl.handle.net/10486/684669 https://dx.doi.org/10.1016/j.amc.2017.11.046 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Projection methods PSPG stabilization Non inf-sup stable elements Matemáticas |
| _version_ | 1878737917560487936 |
|---|---|
| author | Frutos, Javier de |
| author2 | García-Archilla, Bosco Novo Martín, Julia |
| author2_role | author author |
| author_browse | Frutos, Javier de García-Archilla, Bosco Novo Martín, Julia |
| author_facet | Frutos, Javier de García-Archilla, Bosco Novo Martín, Julia |
| author_role | author |
| collection | Biblos-e Archivo. Repositorio Institucional de la UAM |
| description | A modified Chorin–Teman (Euler non-incremental) projection method and a modified Euler incremental projection method for non inf-sup stable mixed finite elements are analyzed. The analysis of the classical Euler non-incremental and Euler incremental methods are obtained as a particular case. We first prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin–Temam method. For the second scheme, we study a stabilization that allows the use of equal-order pairs of finite elements. The relation of the methods with the so-called pressure stabilized Petrov Galerkin method (PSPG) is established. The influence of the chosen initial approximations in the computed approximations to the pressure is analyzed. Numerical tests confirm the theoretical results |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_a6e94d05ecebadd9f5c59bb1a83f4cbe |
| institution | Universidad Autónoma de Madrid |
| instname_str | Universidad Autónoma de Madrid |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:repositorio.uam.es:10486/684669 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | Biblos-e Archivo. Repositorio Institucional de la UAM |
| spelling | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem Frutos, Javier de García-Archilla, Bosco Novo Martín, Julia Projection methods PSPG stabilization Non inf-sup stable elements Matemáticas A modified Chorin–Teman (Euler non-incremental) projection method and a modified Euler incremental projection method for non inf-sup stable mixed finite elements are analyzed. The analysis of the classical Euler non-incremental and Euler incremental methods are obtained as a particular case. We first prove that the modified Euler non-incremental scheme has an inherent stabilization that allows the use of non inf-sup stable mixed finite elements without any kind of extra added stabilization. We show that it is also true in the case of the classical Chorin–Temam method. For the second scheme, we study a stabilization that allows the use of equal-order pairs of finite elements. The relation of the methods with the so-called pressure stabilized Petrov Galerkin method (PSPG) is established. The influence of the chosen initial approximations in the computed approximations to the pressure is analyzed. Numerical tests confirm the theoretical results Research sup-ported by Spanish MINECO under grants MTM2013-42538-P (MINECO, ES) and MTM2016-78995-P (AEI/FEDER UE) Elsevier http://hdl.handle.net/10486/684669 https://dx.doi.org/10.1016/j.amc.2017.11.046 |
| spellingShingle | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem Frutos, Javier de Projection methods PSPG stabilization Non inf-sup stable elements Matemáticas |
| title | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| title_full | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| title_fullStr | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| title_full_unstemmed | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| title_short | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| title_sort | Error analysis of projection methods for non inf-sup stable mixed finite elements: The transient Stokes problem |
| topic | Projection methods PSPG stabilization Non inf-sup stable elements Matemáticas |
| topic_facet | Projection methods PSPG stabilization Non inf-sup stable elements Matemáticas |
| url | http://hdl.handle.net/10486/684669 https://dx.doi.org/10.1016/j.amc.2017.11.046 |