| Issue |
ESAIM: M2AN
Volume 45, Number 2, March-April 2011
|
|
|---|---|---|
| Page(s) | 201 - 216 | |
| DOI | https://doi.org/10.1051/m2an/2010038 | |
| Published online | 02 August 2010 | |
A penalty algorithm for the spectral element discretization of the Stokes problem*
1
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
2
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
3
Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia. nejmeddine.chorfi@fst.rnu.tn
4
Faculté des Sciences de Bizerte, ENIT-LAMSIN, B.P. 37, 1002 Tunis Le Belvédère, Tunisia. nizar.kharrat@enit.rnu.tn
Received:
18
June
2008
Revised:
18
September
2009
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.
Mathematics Subject Classification: 76D07 / 76M22
Key words: Stokes problem / spectral elements / penalty algorithm
© EDP Sciences, SMAI, 2010
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