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: Yongdeok Kim, Sungyun Lee
Format: Article
Language:English
Published: Wiley 2000-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171200002908
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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
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issn 0161-1712
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publishDate 2000-01-01
publisher Wiley
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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