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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2014

On discrete functional inequalities for some finite volume schemes

Résumé

We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincaré-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space $BV(\Omega)$ into $L^{N/(N-1)}(\Omega)$ for a Lipschitz domain $ \Omega \subset \mathbb{R}^{N}$, with $N \geq 2$. 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.
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Dates et versions

hal-00672591 , version 1 (21-02-2012)
hal-00672591 , version 2 (21-02-2012)
hal-00672591 , version 3 (15-01-2014)

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Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Francis Filbet. On discrete functional inequalities for some finite volume schemes. IMA Journal of Numerical Analysis, 2014, pp.10-32. ⟨10.1093/imanum/dru032⟩. ⟨hal-00672591v3⟩
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