Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system - ANR - Agence nationale de la recherche Accéder directement au contenu
Article Dans Une Revue SMAI Journal of Computational Mathematics Année : 2017

Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system

Résumé

In this paper, a nonlinear control volume finite element (CVFE) scheme for a degenerate Keller--Segel model with anisotropic and heterogeneous diffusion tensors is proposed and analyzed. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in finite element methods. The diffusion term which involves an anisotropic and heterogeneous tensor is discretized on a dual mesh (Donald mesh) using the diffusion fluxes provided by the conforming finite element reconstruction on the primal mesh. The other terms are discretized using a nonclassical upwind finite volume scheme on the dual mesh. The scheme ensures the validity of the discrete maximum principle without any restriction on the transmissibility coefficients. The convergence of the scheme is proved under very general assumptions. Finally, some numerical experiments are carried out to prove the ability of the scheme to tackle degenerate anisotropic and heterogeneous diffusion problems over general meshes.
Fichier principal
Vignette du fichier
Nonlinear CVFE for chemotaxis.pdf (794.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01119210 , version 1 (24-02-2015)

Licence

Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales

Identifiants

Citer

Clément Cancès, Moustafa Ibrahim, Mazen Saad. Positive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system. SMAI Journal of Computational Mathematics, 2017, 3, pp.1--28. ⟨10.5802/smai-jcm.18⟩. ⟨hal-01119210⟩
1952 Consultations
354 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More