On discrete functional inequalities for some finite volume schemes

Details On discrete functional inequalities for some finite volume schemes On discrete functional inequalities for some finite volume schemes

2012-02-22

arxiv.org/abs/1202.4860v1

Mathematics

Numerical Analysis

Scientific paper

We prove several discrete Gagliardo-Nirenberg-Sobolev and Sobolev-Poincar\'e inequalities 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(\Omega) into LN/(N-1)(\Omega) for a Lipschitz domain \Omega \subset RN, 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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