Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

Numerical analysis of a robust free energy 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 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.
Fichier principal
Vignette du fichier
VAGNL-Hal-v2.pdf (1.63 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

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)

Identifiants

Citer

Clément Cancès, Cindy Guichard. Numerical analysis of a robust free energy diminishing Finite Volume scheme for parabolic equations with gradient structure. 2016. ⟨hal-01119735v3⟩
708 Consultations
638 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More