Stable finite element methods for the Stokes problem
The mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergen...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200002908 |
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| _version_ | 1849691567282978816 |
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| author | Yongdeok Kim Sungyun Lee |
| author_facet | Yongdeok Kim Sungyun Lee |
| author_sort | Yongdeok Kim |
| collection | DOAJ |
| description | The mixed finite element scheme of the Stokes problem with
pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the
macroelement technique. The order of convergence follows from the standard
theory of mixed methods. The macroelement technique can also be applicable
to the stability analysis for some higher order methods using continuous
pressures such as Taylor-Hood methods, cross-grid methods, or iso-grid
methods. |
| format | Article |
| id | doaj-art-e215c6007a4b4b2fb0c82ec1975674fc |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e215c6007a4b4b2fb0c82ec1975674fc2025-08-20T03:20:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01241069971410.1155/S0161171200002908Stable finite element methods for the Stokes problemYongdeok Kim0Sungyun Lee1Department of Mathematics, KAIST, Taejon 305-701, KoreaDepartment of Mathematics, KAIST, Taejon 305-701, KoreaThe mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-grid Pk−Pk−1elements, k≥1, using discontinuous pressures. The Pk+−Pk−1 elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergence follows from the standard theory of mixed methods. The macroelement technique can also be applicable to the stability analysis for some higher order methods using continuous pressures such as Taylor-Hood methods, cross-grid methods, or iso-grid methods.http://dx.doi.org/10.1155/S0161171200002908Mixed finite element methodstabilizationStokes problem. |
| spellingShingle | Yongdeok Kim Sungyun Lee Stable finite element methods for the Stokes problem International Journal of Mathematics and Mathematical Sciences Mixed finite element method stabilization Stokes problem. |
| title | Stable finite element methods for the Stokes problem |
| title_full | Stable finite element methods for the Stokes problem |
| title_fullStr | Stable finite element methods for the Stokes problem |
| title_full_unstemmed | Stable finite element methods for the Stokes problem |
| title_short | Stable finite element methods for the Stokes problem |
| title_sort | stable finite element methods for the stokes problem |
| topic | Mixed finite element method stabilization Stokes problem. |
| url | http://dx.doi.org/10.1155/S0161171200002908 |
| work_keys_str_mv | AT yongdeokkim stablefiniteelementmethodsforthestokesproblem AT sungyunlee stablefiniteelementmethodsforthestokesproblem |