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A penalty algorithm for the spectral element discretization of the Stokes problem*

Published online by Cambridge University Press:  02 August 2010

Christine Bernardi,
Adel Blouza,
Nejmeddine Chorfi and
Nizar Kharrat
Christine Bernardi
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France. bernardi@ann.jussieu.fr
Adel Blouza
Affiliation:
Laboratoire de Mathématiques Raphaël Salem (U.M.R. 6085 C.N.R.S.), Université de Rouen, avenue de l'Université, B.P. 12, 76801 Saint-Étienne-du-Rouvray, France. Adel.Blouza@univ-rouen.fr
Nejmeddine Chorfi
Affiliation:
Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia. nejmeddine.chorfi@fst.rnu.tn
Nizar Kharrat
Affiliation:
Faculté des Sciences de Bizerte, ENIT-LAMSIN, B.P. 37, 1002 Tunis Le Belvédère, Tunisia. nizar.kharrat@enit.rnu.tn

Abstract

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The penalty method when applied to the Stokes problem provides a very efficient algorithm for solving any discretization of this problem since it gives rise to a system of two equations where the unknowns are uncoupled. For a spectral or spectral element discretization of the Stokes problem, we prove a posteriori estimates that allow us to optimize the penalty parameter as a function of the discretization parameter. Numerical experiments confirm the interest of this technique.

Keywords

Stokes problemspectral elementspenalty algorithm

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 2 , March 2011, pp. 201 - 216
Copyright
© EDP Sciences, SMAI, 2010

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