On discrete functional inequalities for some finite volume schemes

2012/02/22 by Marianne Bessemoulin‐Chatard, Bessemoulin-Chatard, Marianne, Claire Chainais-Hillairet +3 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1202.4860

openalex publication_date 2012/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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^N/(N-1)(Ω) for a Lipschitz domain Ω⊂ ℝ^N, 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.

Citations

• Exact Price of Anarchy for Polynomial Congestion Games

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