Analyse numérique
A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators
[Une combinaison d’ordre 2 de méthodes vérifiant un principe du maximum pour la discrétisation d’opérateurs de diffusion]
Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 89-95.

Nous décrivons une combinaison d’ordre 2 de méthodes supprimant les oscillations apparaissant pour la discrétisation d’opérateur de diffusion avec des schémas volumes finis centrés sur les mailles.

We describe a second order in space combination of methods suppressing oscillations appearing for diffusion operator discretization with cell-centered finite volume schemes.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.15
Le Potier, Christophe 1

1 CEA-Saclay, DEN, DM2S, STMF, LMEC, F-91191 Gif-sur-Yvette, France
@article{CRMATH_2020__358_1_89_0,
     author = {Le Potier, Christophe},
     title = {A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {89--95},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.15},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.15/}
}
TY  - JOUR
AU  - Le Potier, Christophe
TI  - A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 89
EP  - 95
VL  - 358
IS  - 1
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.15/
DO  - 10.5802/crmath.15
LA  - en
ID  - CRMATH_2020__358_1_89_0
ER  - 
%0 Journal Article
%A Le Potier, Christophe
%T A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators
%J Comptes Rendus. Mathématique
%D 2020
%P 89-95
%V 358
%N 1
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.15/
%R 10.5802/crmath.15
%G en
%F CRMATH_2020__358_1_89_0
Le Potier, Christophe. A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 89-95. doi : 10.5802/crmath.15. http://www.numdam.org/articles/10.5802/crmath.15/

[1] Aavatsmark, I.; Barkve, T.; Bøe, O.; Mannseth, T. Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods, SIAM J. Sci. Comput., Volume 19 (1998) no. 5, pp. 1700-1716 | DOI | Zbl

[2] Agelas, Léo; Eymard, Robert; Herbin, Raphaèle A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media, C. R. Math. Acad. Sci. Paris, Volume 347 (2009) no. 11-12, pp. 673-676 | DOI | MR | Zbl

[3] Agelas, Léo; Masson, Roland Convergence of the finite volume MPFA O scheme for heterogeneous anisotropic diffusion problems on general meshes, C. R. Math. Acad. Sci. Paris, Volume 346 (2008) no. 17-18, pp. 1007-1012 | DOI | MR | Zbl

[4] Boyer, Franck; Hubert, Florence Finite volume method for 2D linear and nonlinear elliptic problems with discontinuities, SIAM J. Numer. Anal., Volume 46 (2008) no. 6, pp. 3032-3070 | DOI | MR | Zbl

[5] Cancès, Clément; Cathala, Mathieu; Le Potier, Christophe Monotone corrections for generic cell-centered Finite Volume approximations of anisotropic diffusion equations, Numer. Math., Volume 125 (2013) no. 3, pp. 387-417 | DOI | MR | Zbl

[6] Cancès, Clément; Chainais-Hillairet, Claire; Krell, Stella Numerical analysis of a nonlinear free-energy diminishing discrete duality finite volume scheme for convection diffusion equations (2017) (https://hal.archives-ouvertes.fr/hal-01529143v1)

[7] Cancès, Clément; Guichard, Cindy Convergence of a nonlinear entropy diminishing Control Volume Finite Element scheme for solving anisotropic degenerate parabolic equations, Math. Comput., Volume 85 (2016) no. 298, pp. 549-580 | DOI | MR | Zbl

[8] Coudiére, Yves; Vila, Jean-Paul; Villedieu, Philippe Convergence Rate of a Finite Volume Scheme for a Two Dimensional Convection Diffusion Problem, M2AN, Math. Model. Numer. Anal., Volume 33 (1999) no. 3, pp. 493-516 | DOI | Numdam | MR | Zbl

[9] Després, Bruno Non linear finite volume schemes for the heat equation in 1D, ESAIM, Math. Model. Numer. Anal., Volume 48 (2014) no. 1, pp. 107-134 | DOI | Zbl

[10] Domelevo, Komla; Omnes, Pascal A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, ESAIM, Math. Model. Numer. Anal., Volume 39 (2005) no. 6, pp. 1203-1249 | DOI | Numdam | MR | Zbl

[11] Droniou, Jérome Finite volume schemes for diffusion equations: introduction to and review of modern methods, Math. Models Methods Appl. Sci., Volume 24 (2014) no. 8, pp. 1575-1619 | DOI | MR | Zbl

[12] Eymard, Robert; Gallouët, T.; Herbin, Raphaèle A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension, IMA J. Numer. Anal., Volume 26 (2006) no. 2, pp. 326-353 | DOI | Zbl

[13] Eymard, Robert; Gallouët, T.; Herbin, Raphaèle Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces, IMA J. Numer. Anal., Volume 30 (2010) no. 4, pp. 1009-1043 | DOI | MR | Zbl

[14] Herbin, Raphaèle; Hubert, Florence Benchmark on discretization schemes for anisotropic diffusion problems on general grids, Finite volumes for complex applications. V. Proceedings of the 5th International Symposium, ISTE, 2008, pp. 659-692 (http://www.latp.univ-mrs.fr/fvca5) | Zbl

[15] Le Potier, Christophe A nonlinear second order in space correction and maximum principle for diffusion operators, C. R. Math. Acad. Sci. Paris, Volume 352 (2014) no. 11, pp. 947-952 | MR | Zbl

[16] Le Potier, Christophe Construction et développement de nouveaux schémas pour des problèmes elliptiques ou paraboliques, 2017 (Habilitation à Diriger des Recherches, https://hal-cea.archives-ouvertes.fr/tel-01788736)

[17] Le Potier, Christophe A nonlinear correction and local minimum principle for diffusion operators with finite differences, C. R. Math. Acad. Sci. Paris, Volume 356 (2018) no. 1, pp. 100-106 | MR | Zbl

[18] Le Potier, Christophe; Mahamane, Amadou A nonlinear correction and maximum principle for diffusion operators discretized using hybrid schemes, C. R. Math. Acad. Sci. Paris, Volume 350 (2012) no. 1-2, pp. 101-106 | DOI | Zbl

[19] Lipnikov, Konstantin; Shashkov, Mikhail; Yotov, Ivan Local flux mimetic finite difference methods, Numer. Math., Volume 112 (2009) no. 1, pp. 115-152 | DOI | MR | Zbl

Cité par Sources :