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| HAL : hal-00567342, version 3 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (21-02-2011) | v2 (22-11-2011) | v3 (23-04-2013) |
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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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| Boris Andreianov 1Mostafa Bendahmane 2 |
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| (20/02/2011) |
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| We present a detailed survey of discrete functional analysis tools (consistency results, Poincaré and Sobolev embedding inequalities, discrete $W^{1,p}$ compactness, discrete compactness in space and in time) for the so-called Discrete Duality (DDFV) Finite Volume schemes in three space dimensions. We concentrate mainly on the 3D CeVe-DDFV scheme presented in [3]. Some of our results are new, such as a general time-compactness result based upon the idea of Kruzhkov [65]; others generalize the ideas known for the 2D DDFV schemes or for traditional two-point finite volume schemes. We illustrate the use of these tools by studying convergence of discretizations of nonlinear elliptic-parabolic problems of Leray-Lions kind, and provide numerical results for this example. |
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| 1 : | Laboratoire de Mathématiques (LM-Besançon) |
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CNRS : UMR6623 – Université de Franche-Comté |
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| 2 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3 : | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| Domaine | : | Mathématiques/Analyse numérique |
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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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| Liste des fichiers attachés à ce document : | |||||
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| hal-00567342, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00567342 | |
| oai:hal.archives-ouvertes.fr:hal-00567342 | |
| Contributeur : Boris Andreianov | |
| Soumis le : Lundi 22 Avril 2013, 21:31:36 | |
| Dernière modification le : Mardi 23 Avril 2013, 09:54:56 | |
