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

Clément Cancès (1) , Cindy Guichard (2, 1)

1 LJLL - Laboratoire Jacques-Louis Lions
2 ANGE - Numerical Analysis, Geophysics and Ecology

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.

Mots clés: Anisotropic parabolic equations; gradient flows; convergence; nonlinear stability; Finite Volume methods

Domaines: Mathématiques [math]

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