FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS - Archive ouverte HAL
Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2014

FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS

Jerome Droniou

Résumé

We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature results, focusing on two important properties of schemes (discrete versions of well-known properties of the continuous equation): coercivity and minimum-maximum principles. Coercivity ensures the stability of the method as well as its convergence under assumptions compatible with real-world applications, whereas minimum-maximum principles are crucial in case of strong anisotropy to obtain physically meaningful approximate solutions.
Fichier principal
Vignette du fichier
m3as-review.pdf (657.44 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00813613 , version 1 (16-04-2013)
hal-00813613 , version 2 (04-06-2013)
hal-00813613 , version 3 (07-02-2014)

Identifiants

Citer

Jerome Droniou. FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS. Mathematical Models and Methods in Applied Sciences, 2014, 24 (8), pp.1575-1619. ⟨10.1142/S0218202514400041⟩. ⟨hal-00813613v3⟩

Collections

TDS-MACS
616 Consultations
6093 Téléchargements

Altmetric

Partager

More