TITLE

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

AUTHOR(S)
Cancès, Clément; Guichard, Cindy
PUB. DATE
December 2017
SOURCE
Foundations of Computational Mathematics;Dec2017, Vol. 17 Issue 6, p1525
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
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.
ACCESSION #
126260801

 

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