A penalty algorithm for the spectral element discretization of the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 2, p. 201-216

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.

DOI : https://doi.org/10.1051/m2an/2010038
Classification:  76D07,  76M22
Keywords: Stokes problem, spectral elements, penalty algorithm
@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},
     publisher = {EDP-Sciences},
     volume = {45},
     number = {2},
     year = {2011},
     pages = {201-216},
     doi = {10.1051/m2an/2010038},
     zbl = {1267.76023},
     mrnumber = {2804636},
     language = {en},
     url = {http://www.numdam.org/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, Volume 45 (2011) no. 2, pp. 201-216. doi : 10.1051/m2an/2010038. http://www.numdam.org/item/M2AN_2011__45_2_201_0/

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