期刊
IMA JOURNAL OF NUMERICAL ANALYSIS
卷 35, 期 3, 页码 1125-1149出版社
OXFORD UNIV PRESS
DOI: 10.1093/imanum/dru032
关键词
discrete functional inequalities; finite volume schemes; mixed boundary conditions; DDFV schemes
资金
- European Research Council (ERC) [2009, 239983-NuSiKiMo]
We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincare-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The key point 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 of R-N, with N >= 2. Finally, we give several applications to discrete duality finite volume schemes which are used for the approximation of nonlinear and nonisotropic elliptic and parabolic problems.
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