| Issue |
ESAIM: M2AN
Volume 51, Number 3, May-June 2017
|
|
|---|---|---|
| Page(s) | 797 - 824 | |
| DOI | https://doi.org/10.1051/m2an/2016036 | |
| Published online | 30 March 2017 | |
A virtual volume method for heterogeneous and anisotropic diffusion-reaction problems on general meshes
IFP Énergies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France.
julien.coatleven@ifpen.fr
Received: 23 October 2015
Revised: 16 March 2016
Accepted: 16 May 2016
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
Key words: Heterogeneous diffusion-reaction problems / finite volumes / general meshes / virtual element method
© EDP Sciences, SMAI 2017
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