On discrete functional inequalities for some finite volume schemes

@inproceedings{BessemoulinChatard2013OnDF,
  title={On discrete functional inequalities for some finite volume schemes},
  author={Marianne Bessemoulin-Chatard and Claire Chainais-Hillairet and Francis Filbet},
  year={2013}
}
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 (Ω) into L (Ω) for a Lipschitz domain Ω ⊂ R , 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. 

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