Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes

J.-L. Guermond

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 3, page 357-374
  • ISSN: 0764-583X

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Guermond, J.-L.. "Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.3 (1994): 357-374. <http://eudml.org/doc/193743>.

@article{Guermond1994,
author = {Guermond, J.-L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {singular perturbations; saddle point problems; preconditioning; Stokes problem; Navier-Stokes equations; convergence; Uzawa operator; finite element; spectral approximations},
language = {fre},
number = {3},
pages = {357-374},
publisher = {Dunod},
title = {Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes},
url = {http://eudml.org/doc/193743},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Guermond, J.-L.
TI - Perturbations singulières des problèmes de point selle et préconditionnement du problème de Stokes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 3
SP - 357
EP - 374
LA - fre
KW - singular perturbations; saddle point problems; preconditioning; Stokes problem; Navier-Stokes equations; convergence; Uzawa operator; finite element; spectral approximations
UR - http://eudml.org/doc/193743
ER -

References

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  1. [1] M. AZAIEZ, 1990, Calcul de la pression dans le problème de Stokes pour les fluides visqueux incompressibles par une méthode spectrale de collocation, Thèse, Université de Paris-Sud. 
  2. [2] M. AZAIEZ, Preconditionning of Stokes problem, en préparation. 
  3. [3] M. AZAIEZ, A. FIKRI, G. LABROSSE, 1992, Direct simulation of 3-D driven cavity flow by collocation spectral method, ICOSAHOM 92, Montpellier. 
  4. [4] C. BERNARDI, Y. MADAY, 1992, Approximations spectrales des problèmes aux limites elliptiques, Mathématiques et Applications 10, Springer-Verlag. Zbl0773.47032MR1208043
  5. [5] H. BREZIS, 1983, Analyse fonctionnelle, théorie et applications, Masson, Paris. Zbl0511.46001MR697382
  6. [6] F. BREZZI, 1974, On the existence uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers, R.A.I.R.O., R. 2, 129-151. Zbl0338.90047MR365287
  7. [7] C. CANUTO, A. QUARTERONI, 1982, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38, 67-86. Zbl0567.41008MR637287
  8. [8] A. CHORIN, 1968, Numerical simulation of the Navier-Stokes equations, Math. Comp., 22, 745-762. Zbl0198.50103MR242392
  9. [9] J. CAHOUET, J.-P. CHABARD, 1988, Some fast 3-D finite element solvers for generalized Stokes problem, Int. J. Num. Meth. in Fluids, 8, 269-295. Zbl0665.76038MR953141
  10. [10] V. GIRAULT, P.-A. RAVIART, 1986, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, 5, Springer-Verlag. Zbl0585.65077MR851383
  11. [11] D. HUET, 1964, Perturbations singulières, C. R. Acad. Sci. Paris, 258, 6320-6322. Zbl0137.29902MR167711
  12. [12] G. LABADIE, P. LASBLEIZ, 1983, Quelques méthodes de résolution du problème de Stokes en éléments finis, E.D.F. rapport HE41/83.01 
  13. [13] J.-L. LIONS, 1973, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, Lecture Notes in Mathematics, 323, Springer-Verlag. Zbl0268.49001MR600331
  14. [14] J.-L. LIONS, E. MAGENES, 1968, Problèmes aux limites non homogènes et applications, Dunod, Paris. Zbl0165.10801
  15. [15] R. TEMAM, 1977, Navier-Stokes Equations, Studies in Mathematics and its Applications, 2, North-Holland. Zbl0383.35057MR609732
  16. [16] R. TEMAM, 1968, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull. Soc. Math. France, 98, 115-152. Zbl0181.18903MR237972

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