Error estimate for finite volume approximate solutions of some oblique derivative boundary value problems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal on Finite Volumes Année : 2006

Error estimate for finite volume approximate solutions of some oblique derivative boundary value problems

Résumé

This paper is an improvment of [BG 05], concerning the Laplace equation with an oblique boundary condition. When the boundary condition involves a regular coefficient, we present a weak formulation of the problem and we prove some existence and uniqueness results of the weak solution. We develop a finite volume scheme and we prove the convergence of the finite volume solution to the weak solution, when the mesh size goes to zero. We also present some partial results for the interesting case of a discontinuous coefficient in the boundary condition. In particular, we give a finite volume scheme, taking in consideration the discontinuities of this coefficient. Finally, we obtain some error estimates (in a convenient norm) of order √ h (where h is the mesh size), when the solution u is regular enough.
Fichier principal
Vignette du fichier
bg-october.pdf (278.12 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-01114201 , version 1 (09-02-2015)

Identifiants

  • HAL Id : hal-01114201 , version 1

Citer

Abdallah Bradji, Thierry Gallouët. Error estimate for finite volume approximate solutions of some oblique derivative boundary value problems. International Journal on Finite Volumes, 2006, 3 (2), pp.1-35. ⟨hal-01114201⟩
152 Consultations
47 Téléchargements

Partager

Gmail Facebook X LinkedIn More