[Estimation a posteriori pour un problème de pollution unidimensionnel en milieu poreux]
On s'intéresse à la discrétisation d'un problème de pollution instationnaire, modélisant le transfert de masse d'un polluant en milieu poreux, par un schéma d'Euler implicite en temps et par volumes finis centrés sur les nœuds en espace. L'estimateur d'erreur a posteriori développé ici est constitué de deux indicateurs d'erreur, le premier lié à la discrétisation temporelle, le second à la discrétisation spatiale.
We are interested in the discretization of a time-dependent pollution problem modeling the mass transfer of contaminant in porous media, by the implicit Euler scheme in time and vertex-centered finite volumes in space. The error estimator consists of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
Accepté le :
Publié le :
@article{CRMATH_2009__347_19-20_1217_0,
author = {Aboulaich, Rajaa and Achchab, Boujem\^aa and Darouichi, Aziz},
title = {A posteriori error estimate for a one-dimensional pollution problem in porous media},
journal = {Comptes Rendus. Math\'ematique},
pages = {1217--1222},
publisher = {Elsevier},
volume = {347},
number = {19-20},
year = {2009},
doi = {10.1016/j.crma.2009.07.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.07.017/}
}
TY - JOUR AU - Aboulaich, Rajaa AU - Achchab, Boujemâa AU - Darouichi, Aziz TI - A posteriori error estimate for a one-dimensional pollution problem in porous media JO - Comptes Rendus. Mathématique PY - 2009 SP - 1217 EP - 1222 VL - 347 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.07.017/ DO - 10.1016/j.crma.2009.07.017 LA - en ID - CRMATH_2009__347_19-20_1217_0 ER -
%0 Journal Article %A Aboulaich, Rajaa %A Achchab, Boujemâa %A Darouichi, Aziz %T A posteriori error estimate for a one-dimensional pollution problem in porous media %J Comptes Rendus. Mathématique %D 2009 %P 1217-1222 %V 347 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.07.017/ %R 10.1016/j.crma.2009.07.017 %G en %F CRMATH_2009__347_19-20_1217_0
Aboulaich, Rajaa; Achchab, Boujemâa; Darouichi, Aziz. A posteriori error estimate for a one-dimensional pollution problem in porous media. Comptes Rendus. Mathématique, Tome 347 (2009) no. 19-20, pp. 1217-1222. doi : 10.1016/j.crma.2009.07.017. http://www.numdam.org/articles/10.1016/j.crma.2009.07.017/
[1] Approximation par volumes finis d'un problème de pollution en milieu poreux, Proceeding of 8th Days of Numerical Analysis and Optimization, ENIM-Rabat, Morocco, 2005
[2] A study of a pollution problem in porous media during vapor extraction, J. Math. Sci.: Adv. Appl., Volume 1 (2008) no. 3, pp. 635-662
[3] R. Aboulaich, B. Achchab, A. Darouichi, A posteriori error analysis in finite volumes approximations for a pollution problem in porous media, Internal report, LERMA, EMI Rabat, 2009
[4] Sur un modèle de pollution en mileux poreux, Maths recherche et application, Volume 2 (2000), pp. 108-120
[5] B. Achchab, A. Agouzal, G.C. Buscaglia, F. Oudin, Adaptive finite volume scheme for elliptic problems, submitted for publication
[6] S. Afilal, Sur un problème d'identification en milieu poreux, Thèse d'Etat, Ecole Mohammadia d'Ingénieurs Rabat, 7 mars 2000
[7] A posteriori analysis of the finite element discretization of some parabolic equations, Math. Comp., Volume 74 (2004) no. 251, pp. 1117-1138
[8] Indicateurs d'erreur pour l'équation de la chaleur, Rev. Européenne Élém. Finis, Volume 9 (2000), pp. 425-438
[9] The finite element method for parabolic problems. II. A posteriori error estimation and adaptive approach, Numer. Math., Volume 40 (1982), pp. 339-371
[10] R. Eymard, T. Gallouet, R. Herbin, Finite volumes method, in: P.G. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, vol. 7, September 1997
[11] An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of parabolic problem, SIAM J. Numer. Anal., Volume 27 (1990), pp. 277-291
[12] A posteriori error estimations of some cell centered finite volume methods for diffusion–convection–reaction problems, SIAM J. Numer. Anal., Volume 44 (2006), pp. 949-978
[13] Adaptive finite elements for a linear parabolic problem, Comput. Methods Appl. Mech. Engrg., Volume 167 (1998), pp. 223-237
[14] Évaporation d'une substance organique dans un milieu poreux, C. R. Acad. Sci. Paris, Sér. II b, Volume 327 (1999), pp. 371-377
[15] Robust a posteriori estimator for advection–diffusion–reaction problems, M2AN, Volume 39 (2005) no. 2, pp. 319-348
[16] A Review of a Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Wiley & Teubner, 1996
[17] A posteriori error estimators for convection–diffusion equations, Numer. Math., Volume 4 (1998), pp. 641-663
[18] A posteriori error estimation techniques for nonlinear elliptic and parabolic PDES, Rev. Européenne Élém. Finis., Volume 9 (2000), pp. 377-402
[19] Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods, Numer. Math., Volume 111 (2008) no. 1, pp. 121-158
Cité par Sources :
☆ This work has been supported in part by the CNRST Morocco, Projet d'établissement Université Hassan 1er Settat, the Volkswagen Foundation: Grant number I/79315, Hydro project and Action Intégrée No MA/05, 115.
