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On 3D DDFV discretization of gradient and divergence operators. II. Discrete functional analysis tools and applications to degenerate parabolic problems.

Boris Andreianov 1, Mostafa Bendahmane 2, Florence Hubert 3

(2011-02-20)

This paper is the sequel of the paper [2] of S. Krell and the authors, where a family of 3D finite volume schemes on ``double'' meshes was constructed and the crucial discrete duality property was established. Heading towards applications, we state some discrete functional analysis tools (consistency results, Poincare and Sobolev embedding inequalities, discrete $W^{1,p}$ compactness, discrete $L^1$ compactness in space and time) for the DDFV scheme of [2]. We apply them to infer convergence of discretizations of nonlinear elliptic-parabolic problems of Leray-Lions kind. Applications to degenerate parabolic-hyperbolic PDEs and to a degenerate parabolic system known in electro-cardiology are briefly discussed.

1:	Laboratoire de Mathématiques (LM-Besançon)
	CNRS : UMR6623 – Université de Franche-Comté
2:	Institut de Mathématiques de Bordeaux (IMB)
	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
3:	Laboratoire d'Analyse, Topologie, Probabilités (LATP)
	CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III

Subject

:

Mathematics/Numerical Analysis

Keyword(s): Finite volume approximation – Discrete duality – CeVe-DDFV – Convergence – Consistency – Discrete compactness – Discrete Sobolev embeddings – Degenerate parabolic problems

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From: Boris Andreianov <>

Submitted on: Sunday, 20 February 2011 21:55:39

Updated on: Monday, 21 February 2011 18:47:19