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 (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 45.2 (2011): 201-216. <http://eudml.org/doc/197386>.

@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},
keywords = {Stokes problem; spectral elements; penalty algorithm},
language = {eng},
month = {1},
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/197386},
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
DA - 2011/1//
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/197386
ER -

References

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  12. G.F. Carey and R. Krishnan, Penalty finite element method for the Navier–Stokes equations. Comput. Meth. Appl. Mech. Eng.42 (1984) 183–224.  
  13. G.F. Carey and R. Krishnan, Convergence of iterative methods in penalty finite element approximation of the Navier–Stokes equations. Comput. Meth. Appl. Mech. Eng.60 (1987) 1–29.  
  14. V. Girault and P.-A. Raviart, Finite Element Methods for Navier–Stokes Equations, Theory and Algorithms . Springer-Verlag (1986).  
  15. Y. Maday, D. Meiron, A.T. Patera and E.M. Rønquist, Analysis of iterative methods for the steady and unsteady Stokes problem: Application to spectral element discretizations. SIAM J. Sci. Comput.14 (1993) 310–337.  
  16. D.S. Malkus and E.T. Olsen, Incompressible finite elements which fail the discrete LBB condition, in Penalty-Finite Element Methods in Mechanics, Phoenix, Am. Soc. Mech. Eng., New York (1982) 33–50.  

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