[Erreurs dʼestimation pour le problème de Stokes en trois dimensions avec des conditions aux limites non standards]
Dans cette Note, nous établissons des estimations dʼerreur a posteriori pour le problème de Stokes avec certaines conditions aux limites non standards en dimension trois. La formulation variationnelle est découplée en un problème pour la vitesse et une équation de Poisson pour la pression. La vitesse est approchée par les éléments finis rot et la pression par les éléments continus standards. Nous établirons par la suite les estimations a posteriori optimales.
This work is devoted to the optimal and a posteriori error estimates of the Stokes problem with some non-standard boundary conditions in three dimensions. The variational formulation is decoupled into a system for the velocity and a Poisson equation for the pressure. The velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. Next, we establish optimal a posteriori estimates.
Accepté le :
Publié le :
@article{CRMATH_2011__349_9-10_523_0,
author = {Hyam Abboud and Fida El Chami and Toni Sayah},
title = {Error estimates for three-dimensional {Stokes} problem with non-standard boundary conditions},
journal = {Comptes Rendus. Math\'ematique},
pages = {523--528},
publisher = {Elsevier},
volume = {349},
number = {9-10},
year = {2011},
doi = {10.1016/j.crma.2011.03.021},
language = {en},
}
TY - JOUR AU - Hyam Abboud AU - Fida El Chami AU - Toni Sayah TI - Error estimates for three-dimensional Stokes problem with non-standard boundary conditions JO - Comptes Rendus. Mathématique PY - 2011 SP - 523 EP - 528 VL - 349 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2011.03.021 LA - en ID - CRMATH_2011__349_9-10_523_0 ER -
%0 Journal Article %A Hyam Abboud %A Fida El Chami %A Toni Sayah %T Error estimates for three-dimensional Stokes problem with non-standard boundary conditions %J Comptes Rendus. Mathématique %D 2011 %P 523-528 %V 349 %N 9-10 %I Elsevier %R 10.1016/j.crma.2011.03.021 %G en %F CRMATH_2011__349_9-10_523_0
Hyam Abboud; Fida El Chami; Toni Sayah. Error estimates for three-dimensional Stokes problem with non-standard boundary conditions. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 523-528. doi : 10.1016/j.crma.2011.03.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.021/
[1] H. Abboud, F. El Chami, T. Sayah, A priori and a posteriori estimates for three-dimensional Stokes equations with nonstandard of boundary conditions, Numerical Methods for Partial Differential Equations, . | DOI
[2] Basic error estimates for elliptic problems, Handbook of Numerical Analysis, vol. II, North-Holland, Amsterdam, 1991
[3] Approximation by finite element functions using local regularization, R.A.I.R.O. Anal. Numer., Volume 9 (1975), pp. 77-84
[4] Curl-conforming finite element methods for Navier–Stokes equations with non-standard boundary conditions in , The Navier–Stokes Equations. Theory and Numerical Methods, Lecture Notes, vol. 1431, Springer, 1990, pp. 201-218
[5] Mixed finite element in , Numer. Math., Volume 35 (1980), pp. 315-341
[6] A mixed finite element method for second order elliptic problems, Mathematical Aspects of Finite Element Methods, Lect. Notes Math., vol. 606, Springer, Berlin, 1977, pp. 292-315
Cité par Sources :
Commentaires - Politique
Numerical simulation of corner singularities: a paradox in Maxwell-like problems
Christophe Hazard
C. R. Méca (2002)
Higher order generalized impedance boundary conditions in electromagnetic scattering problems
Marc Duruflé; Houssem Haddar; Patrick Joly
C. R. Phys (2006)