Pré-Publication, Document De Travail Année : 2015

Numerical analysis of a robust entropy-diminishing Finite Volume scheme for parabolic equations with gradient structure

Résumé

We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves the formal gradient flow structure at the discrete level. The existence of a solution to and the convergence of the scheme are proved under very general assumptions on the continuous problem (nonlinearities, anisotropy, heterogeneity) and on the mesh. We also provide numerical evidences of the efficiency and of the robustness of our approach.

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Dates et versions

hal-01119735 , version 1 (24-02-2015)
hal-01119735 , version 2 (18-03-2015)
hal-01119735 , version 3 (10-02-2016)
hal-01119735 , version 4 (07-07-2016)

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  • HAL Id : hal-01119735 , version 1

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Clément Cancès, Cindy Guichard. Numerical analysis of a robust entropy-diminishing Finite Volume scheme for parabolic equations with gradient structure. 2015. ⟨hal-01119735v1⟩
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