Un schéma linéaire vérifiant le principe du maximum pour des opérateurs de diffusion très anisotropes sur des maillages déformés

Comptes Rendus Mathematique - Tập 347 - Trang 105-110 - 2009
Christophe Le Potier1
1Commissariat à l'énergie atomique, DEN/DM2S/SFME, 91191 Gif-Sur-Yvette cedex, France

Tài liệu tham khảo

Bernard-Michel, 2004, The Andra Couplex1 test: comparisons between finite element, mixed hybrid finite element and finite volume element discretizations: simulation of transport around a nuclear waste disposal site, Comput. Geosci., 8, 187, 10.1023/B:COMG.0000035079.68284.49 Burman, 2004, Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes, C. R. Acad. Sci. Paris, Ser. I, 338, 641, 10.1016/j.crma.2004.02.010 F. Dabbène, Mixed hybrid finite elements for transport of polluants by undergrounds water, in: Proceeding of the 10th International Conference on Finite Elements in Fluids, Tucson, USA, 1998 Dantzig, 1951, Maximization of a linear function of variables subject to linear inequalities, 339 Eymard, 2000, Finite volume method, vol. VII I. Faille, Modélisation bidimensonnelle de la génèse et de la migration des hydrocarbures dans un bassin sédimentaire, Thèse de l'université Joseph Fourier-Grenoble 1, 1992 Gavete, 2003, Improvements of generalized finite difference method and comparison with other meshless method, Appl. Math. Modelling, 27, 831, 10.1016/S0307-904X(03)00091-X A. Genty, C. Le Potier, Avoiding negative concentrations for transport calculations of radionuclides in high-level radioactive waste disposal system, in: IAHR, International Groundwater Symposium, Istanbul, 2008, pp. 286–292 Herbin Le Potier, 2005, Finite volume scheme for highly anisotropic diffusion operators on unstructured meshes, C. R. Acad. Sci. Paris, Ser. I, 340, 921, 10.1016/j.crma.2005.05.011 Le Potier, 2005, Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes, C. R. Acad. Sci. Paris, Ser. I, 341, 787, 10.1016/j.crma.2005.10.010 C. Le Potier, Finite volume scheme satisfying maximum and minimum principles for anisotropic diffusion operators, in: Finite Volumes for Complex Applications V, Aussois, 2008, pp. 103–118 Xu, 1999, A monotone finite element scheme for convection–diffusion equations, Math. Comp., 66, 1429, 10.1090/S0025-5718-99-01148-5