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Published in: Foundations of Computational Mathematics 6/2017

25-08-2016

Numerical Analysis of a Robust Free Energy Diminishing Finite Volume Scheme for Parabolic Equations with Gradient Structure

Authors: Clément Cancès, Cindy Guichard

Published in: Foundations of Computational Mathematics | Issue 6/2017

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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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Appendix
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Metadata
Title
Numerical Analysis of a Robust Free Energy Diminishing Finite Volume Scheme for Parabolic Equations with Gradient Structure
Authors
Clément Cancès
Cindy Guichard
Publication date
25-08-2016
Publisher
Springer US
Published in
Foundations of Computational Mathematics / Issue 6/2017
Print ISSN: 1615-3375
Electronic ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-016-9328-6

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