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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, Poincaré 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, and illustrate them with numerical results. 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: Tuesday, 22 November 2011 18:41:56

Updated on: Tuesday, 22 November 2011 18:49:44