Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy - ANR - Agence nationale de la recherche Accéder directement au contenu
Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2018

Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy

Résumé

We extend the nonlinear Control Volume Finite Element scheme of [C. Cancès and C. Guichard, Math. Comp., 85(298):549-580, 2016] to the discretization of Richards equation. This scheme ensures the preservation of the physical bounds without any restriction on the mesh and on the anisotropy tensor. Moreover, it does not require the introduction of the so-called Kirchhoff transform in its definition. It also provides a control on the capillary energy. Based on this nonlinear stability property, we show that the scheme converges towards the unique solution to Richards equation when the discretization parameters tend to 0. Finally we present some numerical experiments to illustrate the behavior of the method.
Fichier principal
Vignette du fichier
CVFE_Richards.pdf (892.19 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01372954 , version 1 (27-09-2016)

Identifiants

Citer

Ahmed Ait Hammou Oulhaj, Clément Cancès, Claire Chainais-Hillairet. Numerical analysis of a nonlinearly stable and positive Control Volume Finite Element scheme for Richards equation with anisotropy. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (4), pp.1532-1567. ⟨10.1051/m2an/2017012⟩. ⟨hal-01372954⟩
731 Consultations
575 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More