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Research report |
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| Subject: |
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Mathematics/Numerical Analysis
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| Title: |
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On 3D DDFV discretization of gradient and divergence operators. II. Discrete functional analysis tools and applications to degenerate parabolic problems. |
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| Author(s): |
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Boris Andreianov ( ) 1, Mostafa Bendahmane () 2, Florence Hubert () 3 |
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| Laboratory: |
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| Abstract: |
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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. |
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| Fulltext language: |
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English |
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| Production date: |
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2011-02-20 |
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| Keyword(s): |
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Finite volume approximation – Discrete duality – CeVe-DDFV – Convergence – Consistency – Discrete compactness – Discrete Sobolev embeddings – Degenerate parabolic problems |
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| Classification: |
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65N12, 65M12 |
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