Gradient schemes: generic tools for the numerical analysis of diffusion equations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2016

Gradient schemes: generic tools for the numerical analysis of diffusion equations

Résumé

The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient scheme framework. These tools enable us to prove that classical schemes are indeed gradient schemes, and allow us to perform a complete and generic study of the well-known (but rarely well-studied) mass lumping process. They also allow an easy check of the mathematical properties of new schemes, by developing a generic process for eliminating unknowns via barycentric condensation, and by designing a concept of discrete functional analysis toolbox for schemes based on polytopal meshes.
Fichier principal
Vignette du fichier
families_hal.pdf (527.28 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01150517 , version 1 (11-05-2015)
hal-01150517 , version 2 (23-08-2015)

Identifiants

  • HAL Id : hal-01150517 , version 2

Citer

Jérôme Droniou, Robert Eymard, Raphaele Herbin. Gradient schemes: generic tools for the numerical analysis of diffusion equations . ESAIM: Mathematical Modelling and Numerical Analysis, 2016, 50 (3), pp.749-781. ⟨hal-01150517v2⟩
494 Consultations
622 Téléchargements

Partager

Gmail Facebook X LinkedIn More