On 3D DDFV discretization of gradient and divergence operators. II. Discrete functional analysis tools and applications to degenerate parabolic problems.
| hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
| dc.contributor.author | ANDREIANOV, Boris | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BENDAHMANE, Mostafa | |
| hal.structure.identifier | Laboratoire d'Analyse, Topologie, Probabilités [LATP] | |
| dc.contributor.author | HUBERT, Florence | |
| dc.date.accessioned | 2024-04-04T02:22:12Z | |
| dc.date.available | 2024-04-04T02:22:12Z | |
| dc.date.created | 2011-02-20 | |
| dc.date.issued | 2013-06 | |
| dc.identifier.issn | 1609-4840 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189635 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | De Gruyter | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.subject.en | Finite volume approximation | |
| dc.subject.en | Discrete duality | |
| dc.subject.en | CeVe-DDFV | |
| dc.subject.en | Convergence | |
| dc.subject.en | Consistency | |
| dc.subject.en | Discrete compactness | |
| dc.subject.en | Discrete Sobolev embeddings | |
| dc.subject.en | Degenerate parabolic problems | |
| dc.title.en | On 3D DDFV discretization of gradient and divergence operators. II. Discrete functional analysis tools and applications to degenerate parabolic problems. | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1515/cmam-2013-0011 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.journal | Computational Methods in Applied Mathematics | |
| bordeaux.page | pp. 369–410 | |
| bordeaux.volume | 13 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00567342 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00567342v1 | |
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