[Adaptation de maillage pour l'équation de convection dispersion stabilisée par la méthode algébrique de sous-mailles orthogonales]
On développe un estimateur d'erreur a posteriori pour l'équation de convection dispersion stabilisée par la méthode algébrique de sous-mailles orthogonales. On obtient une majoration et une minoration de l'erreur. Les résultats numériques montre l'efficacité de l'indicateur d'erreur dans les régions des singularités où la solution présente des couches limites.
We derive a residual a posteriori error estimator for the algebraic orthogonal subscales stabilization of convective dispersive transport equation. The estimator yields upper bound on the error which is global and lower bound that is local. Numerical studies show the behaviour of the error indicator and how it is robust to deal with singularities.
Accepté le :
Publié le :
@article{CRMATH_2008__346_21-22_1187_0,
author = {Boujema\^a Achchab and Mohamed El Fatini and Alexandre Ern and A. Souissi},
title = {Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport},
journal = {Comptes Rendus. Math\'ematique},
pages = {1187--1190},
publisher = {Elsevier},
volume = {346},
number = {21-22},
year = {2008},
doi = {10.1016/j.crma.2008.09.016},
language = {en},
}
TY - JOUR AU - Boujemaâ Achchab AU - Mohamed El Fatini AU - Alexandre Ern AU - A. Souissi TI - Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport JO - Comptes Rendus. Mathématique PY - 2008 SP - 1187 EP - 1190 VL - 346 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2008.09.016 LA - en ID - CRMATH_2008__346_21-22_1187_0 ER -
%0 Journal Article %A Boujemaâ Achchab %A Mohamed El Fatini %A Alexandre Ern %A A. Souissi %T Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport %J Comptes Rendus. Mathématique %D 2008 %P 1187-1190 %V 346 %N 21-22 %I Elsevier %R 10.1016/j.crma.2008.09.016 %G en %F CRMATH_2008__346_21-22_1187_0
Boujemaâ Achchab; Mohamed El Fatini; Alexandre Ern; A. Souissi. Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1187-1190. doi : 10.1016/j.crma.2008.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.09.016/
[1] B. Achchab, M. El Fatini, A. Ern, A. Souissi, A posteriori error estimates for subgrid viscosity stabilized approximations of convection–diffusion equations, Appl. Math. Lett. (2008), submitted for publication
[2] D. Bernardi, F. Hecht, K. Ohtsuka, O. Pironneau, FreeFem+ for Macs, Pcs, Linux (Dec 25 2008) http://www.freefem.org
[3] Choosing bubbles for advection–diffusion problems, Math. Models Methods Appl. Sci., Volume 4 (1994), pp. 571-587
[4] Streamline upwind/Petrov Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations, Model. Comput. Methods Appl. Mech. Engrg., Volume 32 (1982) no. 1-3, p. 199
[5] The Finite Element Methods for Elliptic Problems, North-Holland, Amsterdam, 1978
[6] Approximation by finite element functions using local regularization, RAIRO, Anal. Numér., Volume 9 (1975), pp. 77-84
[7] On stabilized finite element methods for linear systems of convection–diffusion–reaction equations, Comp. Meth. Appl. Mech. Engrg., Volume 188 (2000), pp. 61-82
[8] Subgrid Stabilization of Galerkin approximations of linear monotone operators, IMA J. Numer. Anal., Volume 21 (2001), pp. 165-197
[9] Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid-scale models, bubbles and the origin of stabilized methods, Comput. Meth. Appl. Mech. Engrg. l, Volume 27 (1995), pp. 387-401
[10] F. Jouve, Xd3d-Version 7.72, Visualisation de maillages 2D et 3D et de surfaces 3D sous X, http://www.cmap.polytechnique.fr
[11] On the transport–diffusion algorithm and its applications to the Navier–Stokes equations, Numer. Math., Volume 38 (1982), pp. 309-332
[12] A posteriori error estimators for convection–diffusion equations, Numer. Math, Volume 80 (1998), pp. 641-663
Cité par Sources :
Commentaires - Politique
A posteriori error estimate for a one-dimensional pollution problem in porous media
Rajaa Aboulaich; Boujemâa Achchab; Aziz Darouichi
C. R. Math (2009)
Estimateur hiérarchique robuste pour un problème de perturbation singulière
Boujemaa Achchab; Said Achchab; Abdellatif Agouzal
C. R. Math (2003)