Comptes Rendus
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, Volume 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
Christophe Le Potier 1

1 CEA-Saclay, DEN, DM2S, STMF, LMEC, F-91191 Gif-sur-Yvette, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2020__358_1_89_0,
     author = {Christophe Le Potier},
     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},
}
TY  - JOUR
AU  - Christophe Le Potier
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
DO  - 10.5802/crmath.15
LA  - en
ID  - CRMATH_2020__358_1_89_0
ER  - 
%0 Journal Article
%A Christophe Le Potier
%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
%R 10.5802/crmath.15
%G en
%F CRMATH_2020__358_1_89_0
Christophe Le Potier. A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 89-95. doi : 10.5802/crmath.15. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.15/

[1] I. Aavatsmark; T. Barkve; O. Bøe; T. Mannseth 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] Léo Agelas; Robert Eymard; Raphaèle Herbin 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] Léo Agelas; Roland Masson 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] Franck Boyer; Florence Hubert 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] Clément Cancès; Mathieu Cathala; Christophe Le Potier 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] Clément Cancès; Claire Chainais-Hillairet; Stella Krell 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] Clément Cancès; Cindy Guichard 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] Yves Coudiére; Jean-Paul Vila; Philippe Villedieu 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] Bruno Després 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] Komla Domelevo; Pascal Omnes 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] Jérome Droniou 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] Robert Eymard; T. Gallouët; Raphaèle Herbin 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] Robert Eymard; T. Gallouët; Raphaèle Herbin 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] Raphaèle Herbin; Florence Hubert 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] Christophe Le Potier 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] Christophe Le Potier 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] Christophe Le Potier 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] Christophe Le Potier; Amadou Mahamane 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] Konstantin Lipnikov; Mikhail Shashkov; Ivan Yotov Local flux mimetic finite difference methods, Numer. Math., Volume 112 (2009) no. 1, pp. 115-152 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Correction non linéaire et principe du maximum pour la discrétisation d'opérateurs de diffusion avec des schémas volumes finis centrés sur les mailles

Christophe Le Potier

C. R. Math (2010)


Correction non linéaire et principe du maximum avec des schémas hybrides pour la discrétisation dʼopérateurs de diffusion

Christophe Le Potier; Amadou Mahamane

C. R. Math (2012)