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

Christine Bernardi; Adel Blouza; Nejmeddine Chorfi; Nizar Kharrat

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2011)

  • Volume: 45, Issue: 2, page 201-216
  • ISSN: 0764-583X

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.

How to cite

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Bernardi, Christine, et al. "A penalty algorithm for the spectral element discretization of the Stokes problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.2 (2011): 201-216. <http://eudml.org/doc/273140>.

@article{Bernardi2011,
abstract = {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.},
author = {Bernardi, Christine, Blouza, Adel, Chorfi, Nejmeddine, Kharrat, Nizar},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Stokes problem; spectral elements; penalty algorithm},
language = {eng},
number = {2},
pages = {201-216},
publisher = {EDP-Sciences},
title = {A penalty algorithm for the spectral element discretization of the Stokes problem},
url = {http://eudml.org/doc/273140},
volume = {45},
year = {2011},
}

TY - JOUR
AU - Bernardi, Christine
AU - Blouza, Adel
AU - Chorfi, Nejmeddine
AU - Kharrat, Nizar
TI - A penalty algorithm for the spectral element discretization of the Stokes problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2011
PB - EDP-Sciences
VL - 45
IS - 2
SP - 201
EP - 216
AB - 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.
LA - eng
KW - Stokes problem; spectral elements; penalty algorithm
UR - http://eudml.org/doc/273140
ER -

References

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