Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection

Abstract : We construct and analyze a discontinuous Galerkin method to solve advection-diffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consistent with well-known results when the problem is either hyperbolic or uniformly elliptic. The theoretical results are supported by numerical evidence.
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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2008, 46 (2), pp.805 - 831. 〈https://epubs.siam.org/doi/10.1137/060676106〉. 〈10.1137/060676106〉
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https://hal.archives-ouvertes.fr/hal-01818201
Contributeur : Daniele Antonio Di Pietro <>
Soumis le : lundi 18 juin 2018 - 18:21:58
Dernière modification le : jeudi 26 juillet 2018 - 11:06:51

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Daniele Antonio Di Pietro, Alexandre Ern, Jean-Luc Guermond. Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2008, 46 (2), pp.805 - 831. 〈https://epubs.siam.org/doi/10.1137/060676106〉. 〈10.1137/060676106〉. 〈hal-01818201〉

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