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Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes

Abstract : We derive new multiple point flux approximations (MPFA) for the finite volume approximation of heterogeneous and anisotropic diffusion problems on general meshes, in dimension 2 and 3. The resulting methods are unconditionally stable while preserving the small stencil typical of MPFA finite volumes. The key idea is to solve local variational problems with a well designed stabilization term from which we deduce conservative flux instead of directly prescribing a flux formula and solving the usual flux continuity equations. The boundary conditions of our local variational problems are handled through additional cell-centered unknowns, leading to an overall scheme with the same number of unknowns than first-order discontinuous Galerkin methods. Convergence results follow from well established frameworks, while numerical experiments illustrate the good behavior of the method.
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https://hal.archives-ouvertes.fr/hal-03728206
Contributor : Julien Coatléven Connect in order to contact the contributor
Submitted on : Wednesday, July 20, 2022 - 10:43:35 AM
Last modification on : Saturday, July 23, 2022 - 3:26:39 AM

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  • HAL Id : hal-03728206, version 1

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Julien Coatléven. Unconditionally stable small stencil enriched multiple point flux approximations of heterogeneous diffusion problems on general meshes. 2022. ⟨hal-03728206⟩

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