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.
@article{M2AN_2011__45_2_201_0,
author = {Bernardi, Christine and Blouza, Adel and Chorfi, Nejmeddine and Kharrat, Nizar},
title = {A penalty algorithm for the spectral element discretization of the Stokes problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {45},
year = {2011},
pages = {201-216},
doi = {10.1051/m2an/2010038},
mrnumber = {2804636},
zbl = {1267.76023},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2011__45_2_201_0}
}
Bernardi, Christine; Blouza, Adel; Chorfi, Nejmeddine; Kharrat, Nizar. A penalty algorithm for the spectral element discretization of the Stokes problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 45 (2011) pp. 201-216. doi : 10.1051/m2an/2010038. http://gdmltest.u-ga.fr/item/M2AN_2011__45_2_201_0/
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