Volume 54, Number 2, March-April 2020
|Page(s)||591 - 618|
|Published online||19 February 2020|
Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations
University of Nice Sophia-Antipolis, LJAD, CNRS UMR 7351, and COFFEE Team, INRIA Sophia Antipolis Méditerran’ee, Parc Valrose, 06108 Nice Cedex 02, France
* Corresponding author: firstname.lastname@example.org
Accepted: 17 October 2019
This article is about the development and the analysis of an enhanced positive control volume finite element scheme for degenerate convection-diffusion type problems. The proposed scheme involves only vertex unknowns and features anisotropic fields. The novelty of the approach is to devise a reliable upwind approximation with respect to flux-like functions for the elliptic term. Then, it is shown that the discrete solution remains nonnegative. Under general assumptions on the data and the mesh, the convergence of the numerical scheme is established owing to a recent compactness argument. The efficiency and stability of the methodology are numerically illustrated for different anisotropic ratios and nonlinearities.
Mathematics Subject Classification: 35K65 / 65M08 / 65M12
Key words: Finite volume / positive / convergence / convection / diffusion
© EDP Sciences, SMAI 2020
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