A finite element method for degenerate two-phase flow in porous media. Part II: Convergence - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Numerical Mathematics Année : 2021

A finite element method for degenerate two-phase flow in porous media. Part II: Convergence

Résumé

Convergence of a finite element method with mass-lumping and flux upwinding is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary unknowns. Well-posedness is obtained in [J. Numer. Math., 29(2), 2021]. Theoretical convergence is proved via a compactness argument. The numerical phase saturation converges strongly to a weak solution in L 2 in space and in time whereas the numerical phase pressures converge strongly to weak solutions in L 2 in space almost everywhere in time. The proof is not straightforward because of the degeneracy of the phase mobilities and the unboundedness of the derivative of the capillary pressure.
Fichier principal
Vignette du fichier
degen.2ph2HAL.pdf (360.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03876363 , version 1 (28-11-2022)

Identifiants

Citer

Vivette Girault, Beatrice Riviere, Loic Cappanera. A finite element method for degenerate two-phase flow in porous media. Part II: Convergence. Journal of Numerical Mathematics, 2021, 29, pp.187-219. ⟨10.1515/jnma-2020-0005⟩. ⟨hal-03876363⟩
9 Consultations
11 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More