A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes.

Abstract : Starting from the recently introduced virtual element method, we construct new diffusion fluxes in two and three dimensions that give birth to symmetric, unconditionally coercive finite volume like schemes for the discretization of heterogeneous and anisotropic diffusion-reaction problems on general, possibly nonconforming meshes. Convergence of the approximate solutions is proved for general tensors and meshes. Error estimates are derived under classical regularity assumptions. Numerical results illustrate the performance of the scheme. The link with the original vertex approximate gradient scheme is emphasized. Mathematics Subject Classification. 65N08, 65N12, 65N15.
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Julien Coatléven. A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes.. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2017, 51 (3), pp.797-824. ⟨10.1051/m2an/2016036⟩. ⟨hal-01581888⟩

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