Local projection stabilized Galerkin approximations for the generalized Stokes problem
We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2009
|
| _version_ | 1797076820164608000 |
|---|---|
| author | Nafa, K Wathen, A |
| author_facet | Nafa, K Wathen, A |
| author_sort | Nafa, K |
| collection | OXFORD |
| description | We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This, makes it a lot simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. © 2008 Elsevier B.V. All rights reserved. |
| first_indexed | 2024-03-07T00:09:11Z |
| format | Journal article |
| id | oxford-uuid:789eb16b-1b3f-4671-b1af-81f42aee4216 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:09:11Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:789eb16b-1b3f-4671-b1af-81f42aee42162022-03-26T20:31:53ZLocal projection stabilized Galerkin approximations for the generalized Stokes problemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:789eb16b-1b3f-4671-b1af-81f42aee4216EnglishSymplectic Elements at Oxford2009Nafa, KWathen, AWe analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although stability of the method has been established, for the homogeneous Stokes equations, the proof given here is based on the existence of a special interpolant with additional orthogonal property with respect to the projection space. This, makes it a lot simpler and more attractive. The resulting stabilized method is shown to lead to optimal rates of convergence for both velocity and pressure approximations. © 2008 Elsevier B.V. All rights reserved. |
| spellingShingle | Nafa, K Wathen, A Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title | Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title_full | Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title_fullStr | Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title_full_unstemmed | Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title_short | Local projection stabilized Galerkin approximations for the generalized Stokes problem |
| title_sort | local projection stabilized galerkin approximations for the generalized stokes problem |
| work_keys_str_mv | AT nafak localprojectionstabilizedgalerkinapproximationsforthegeneralizedstokesproblem AT wathena localprojectionstabilizedgalerkinapproximationsforthegeneralizedstokesproblem |