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Journal Articles Foundations of Computational Mathematics Year : 2017

Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure

Abstract

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 at the discrete level the formal gradient flow structure, allowing the use of some nonlinear test functions in the analysis. 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. Moreover, we provide numerical evidences of the efficiency and of the robustness of our approach.
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Dates and 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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Clément Cancès, Cindy Guichard. Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure. Foundations of Computational Mathematics, 2017, 17 (6), pp.1525-1584. ⟨10.1007/s10208-016-9328-6⟩. ⟨hal-01119735v4⟩
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