Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem

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In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained b...

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Autores principales: Armentano, M.G., Blasco, J.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Materias:
Cross-grid
Macroelement technique
Mixed finite elements
Stability analysis
Stokes problem
A-stability
Finite Element
Macro element
Mixed finite element methods
Numerical results
Numerical solution
Pressure modes
Triangular meshes
Two space dimensions
Numerical methods
Stability
Finite element method
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03770427_v234_n5_p1404_Armentano
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_03770427_v234_n5_p1404_Armentano2023-06-12T16:47:58Z Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem J. Comput. Appl. Math. 2010;234(5):1404-1416 Armentano, M.G. Blasco, J. Cross-grid Macroelement technique Mixed finite elements Stability analysis Stokes problem A-stability Finite Element Macro element Mixed finite element methods Mixed finite elements Numerical results Numerical solution Pressure modes Stability analysis Stokes problem Triangular meshes Two space dimensions Numerical methods Stability Finite element method In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid Pk Ql. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1 Q1 and P2 Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1 Q1 element and the stability of the P2 Q1 element. © 2010 Elsevier B.V. All rights reserved. Fil:Armentano, M.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03770427_v234_n5_p1404_Armentano
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Cross-grid
Macroelement technique
Mixed finite elements
Stability analysis
Stokes problem
A-stability
Finite Element
Macro element
Mixed finite element methods
Mixed finite elements
Numerical results
Numerical solution
Pressure modes
Stability analysis
Stokes problem
Triangular meshes
Two space dimensions
Numerical methods
Stability
Finite element method
spellingShingle Cross-grid
Macroelement technique
Mixed finite elements
Stability analysis
Stokes problem
A-stability
Finite Element
Macro element
Mixed finite element methods
Mixed finite elements
Numerical results
Numerical solution
Pressure modes
Stability analysis
Stokes problem
Triangular meshes
Two space dimensions
Numerical methods
Stability
Finite element method
Armentano, M.G.
Blasco, J.
Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
topic_facet Cross-grid
Macroelement technique
Mixed finite elements
Stability analysis
Stokes problem
A-stability
Finite Element
Macro element
Mixed finite element methods
Mixed finite elements
Numerical results
Numerical solution
Pressure modes
Stability analysis
Stokes problem
Triangular meshes
Two space dimensions
Numerical methods
Stability
Finite element method
description In this paper we develop and analyze a family of mixed finite element methods for the numerical solution of the Stokes problem in two space dimensions. In these schemes, the pressure is interpolated on a mesh of rectangular elements, while the velocity is approximated on a triangular mesh obtained by dividing each rectangle into four triangles by its diagonals. Continuous interpolations of degrees k for the velocity and l for the pressure are considered, so the new finite elements are called cross-grid Pk Ql. A stability analysis of these approximations is provided, based on the macroelement technique of Stenberg. The lowest order P1 Q1 and P2 Q1 cases are analyzed in detail; in the first case, a global spurious pressure mode is shown to exist, so this element is unstable. In the second case, however, stability is rigorously proved. Numerical results obtained in these two cases are also presented, which confirm the existence of the spurious pressure mode for the P1 Q1 element and the stability of the P2 Q1 element. © 2010 Elsevier B.V. All rights reserved.
format Artículo
Artículo
publishedVersion
author Armentano, M.G.
Blasco, J.
author_facet Armentano, M.G.
Blasco, J.
author_sort Armentano, M.G.
title Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
title_short Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
title_full Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
title_fullStr Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
title_full_unstemmed Stable and unstable cross-grid Pk Ql mixed finite elements for the Stokes problem
title_sort stable and unstable cross-grid pk ql mixed finite elements for the stokes problem
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_03770427_v234_n5_p1404_Armentano
work_keys_str_mv AT armentanomg stableandunstablecrossgridpkqlmixedfiniteelementsforthestokesproblem
AT blascoj stableandunstablecrossgridpkqlmixedfiniteelementsforthestokesproblem
_version_ 1769810121369583616

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