On discrete functional inequalities for some finite volume schemes
Résumé
We prove several discrete Gagliardo-Nirenberg-Sobolev and Sobolev-Poincar ́e inequali- ties for some approximations with arbitrary boundary values on finite volume admissible meshes. The keypoint of our approach is to use the continuous embedding of the space BV(Ω) into LN/(N−1)(Ω) for a Lipschitz domain Ω ⊂ RN, with N ≥ 2. Finally, we give several applications to discrete duality finite volume (DDFV) schemes which are used for the approximation of nonlinear and non isotropic elliptic and parabolic problems.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)