no. 2
A penalty algorithm for the spectral element discretization of the Stokes problem
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 45 (2011) no. 2, pp. 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 : 10.1051/m2an/2010038
Classification : 76D07, 76M22
Mots clés : Stokes problem, spectral elements, penalty algorithm 
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     title = {A penalty algorithm for the spectral element discretization of the {Stokes} problem},
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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 , Tome 45 (2011) no. 2, pp. 201-216. doi : 10.1051/m2an/2010038. http://www.numdam.org/articles/10.1051/m2an/2010038/

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