Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations - ANR - Agence nationale de la recherche Accéder directement au contenu
Article Dans Une Revue Computational Methods in Applied Mathematics Année : 2018

Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations

Résumé

We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation relation. This relation is of paramount importance to capture the long-time behavior of the problem in an accurate way. To enforce it, the linear convection diffusion equation is rewritten in a nonlinear form before being discretized. We establish the existence of positive solutions to the scheme. Based on compactness arguments, the convergence of the approximate solution towards a weak solution is established. Finally, we provide numerical evidences of the good behavior of the scheme when the discretization parameters tend to 0 and when time goes to infinity.
Fichier principal
Vignette du fichier
nlDDFV_preprint.pdf (789.17 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01529143 , version 1 (30-05-2017)

Identifiants

Citer

Clément Cancès, Claire Chainais-Hillairet, Stella Krell. Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations. Computational Methods in Applied Mathematics, 2018, 18 (3), pp.407-432. ⟨10.1515/cmam-2017-0043⟩. ⟨hal-01529143⟩
487 Consultations
451 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More