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Eymard, Robert; Gallouët, Thierry; Herbin, Raphaèle

A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis. (English) Zbl 1112.65120

C. R., Math., Acad. Sci. Paris 344, No. 6, 403-406 (2007).
Summary: We introduce here a new finite volume scheme which was developed for the discretization of anisotropic diffusion problems; the originality of this scheme lies in the fact that we are able to prove its convergence under very weak assumptions on the discretization mesh.

Cited in 28 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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\textit{R. Eymard} et al., C. R., Math., Acad. Sci. Paris 344, No. 6, 403--406 (2007; Zbl 1112.65120)
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References:

[1] Coudière, Y.; Gallouët, T.; Herbin, R., Discrete Sobolev inequalities and \(L_p\) error estimates for finite volume solutions of convection diffusion equations, M2AN math. model. numer. anal., 35, 4, 767-778, (2001) · Zbl 0990.65122
[2] Coudière, Y.; Vila, J.-P.; Villedieu, Ph., Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem, M2AN math. model. numer. anal., 33, 3, 493-516, (1999) · Zbl 0937.65116
[3] Domelevo, K.; Omnes, P., A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids, M2AN math. model. numer. anal., 39, 6, 1203-1249, (2005) · Zbl 1086.65108
[4] Eymard, R.; Gallouët, T., H-convergence and numerical schemes for elliptic equations, SIAM J. numer. anal., 41, 2, 539-562, (2000) · Zbl 1049.35015
[5] Eymard, R.; Gallouët, T.; Herbin, R., A cell-centered finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension, IMA J. numer. anal., 26, 2, 326-353, (2006) · Zbl 1093.65110
[6] Herbin, R., An error estimate for a finite volume scheme for a diffusion – convection problem on a triangular mesh, Numer. methods partial differential equations, 11, 2, 165-173, (1995) · Zbl 0822.65085
[7] Le Potier, C., Schéma volumes finis pour des opérateurs de diffusion fortement anisotropes sur des maillages non structurés, C. R. math. acad. sci. Paris, ser. I, 340, 12, 921-926, (2005) · Zbl 1076.76049
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