On propose une méthode de Galerkine centrée aux mailles avec stencil compact et stabilisation de sous-grille pour des problèmes de diffusion anisotrope et hétérogène. On présente à la fois les résultats théoriques essentiels et une validation numérique.
In this work we propose a compact cell-centered Galerkin method with subgrid stabilization for anisotropic heterogeneous diffusion problems on general meshes. Both essential theoretical results and numerical validation are provided.
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@article{CRMATH_2011__349_1-2_93_0, author = {Di Pietro, Daniele A.}, title = {A compact cell-centered {Galerkin} method with subgrid stabilization}, journal = {Comptes Rendus. Math\'ematique}, pages = {93--98}, publisher = {Elsevier}, volume = {349}, number = {1-2}, year = {2011}, doi = {10.1016/j.crma.2010.11.017}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2010.11.017/} }
TY - JOUR AU - Di Pietro, Daniele A. TI - A compact cell-centered Galerkin method with subgrid stabilization JO - Comptes Rendus. Mathématique PY - 2011 SP - 93 EP - 98 VL - 349 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.11.017/ DO - 10.1016/j.crma.2010.11.017 LA - en ID - CRMATH_2011__349_1-2_93_0 ER -
%0 Journal Article %A Di Pietro, Daniele A. %T A compact cell-centered Galerkin method with subgrid stabilization %J Comptes Rendus. Mathématique %D 2011 %P 93-98 %V 349 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.11.017/ %R 10.1016/j.crma.2010.11.017 %G en %F CRMATH_2011__349_1-2_93_0
Di Pietro, Daniele A. A compact cell-centered Galerkin method with subgrid stabilization. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 93-98. doi : 10.1016/j.crma.2010.11.017. http://www.numdam.org/articles/10.1016/j.crma.2010.11.017/
[1] A compact multipoint flux approximation method with improved robustness, Numer. Methods Partial Differential Equations, Volume 24 (2008) no. 5, pp. 1329-1360 | DOI
[2] The G method for heterogeneous anisotropic diffusion on general meshes, M2AN Math. Model. Numer. Anal., Volume 44 (2010) no. 4, pp. 597-625 | DOI
[3] An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes, IJFV, Volume 7 (2010) no. 1, pp. 1-29
[4] Cell centered Galerkin methods, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 31-34 | DOI
[5] Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection, SIAM J. Numer. Anal., Volume 46 (2008) no. 2, pp. 805-831 | DOI
[6] Unstructured control-volume distributed full tensor finite volume schemes with flow based grids, Comput. Geosci., Volume 6 (2002) no. 10, pp. 433-452 | DOI
[7] 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 | DOI
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