On 3D DDFV discretization of gradient and divergence operators. I. Meshing, operators and discrete duality.
| hal.structure.identifier | Laboratoire de Mathématiques de Besançon (UMR 6623) [LMB] | |
| dc.contributor.author | ANDREIANOV, Boris | |
| hal.structure.identifier | Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA] | |
| 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 | |
| hal.structure.identifier | Laboratoire Jean Alexandre Dieudonné [LJAD] | |
| hal.structure.identifier | Laboratoire d'Analyse, Topologie, Probabilités [LATP] | |
| hal.structure.identifier | SImulations and Modeling for PArticles and Fluids [SIMPAF] | |
| dc.contributor.author | KRELL, Stella | |
| dc.date.accessioned | 2024-04-04T02:27:08Z | |
| dc.date.available | 2024-04-04T02:27:08Z | |
| dc.date.created | 2011-03-11 | |
| dc.date.issued | 2012-10-12 | |
| dc.identifier.issn | 0272-4979 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190004 | |
| dc.description.abstractEn | This work is intended to provide a convenient tool for the mathematical analysis of a particular kind of finite volume approximation which can be used, for instance, in the context of nonlinear and/or anisotropic diffusion operators in 3D. Following the approach developed by F. Hermeline and by K.~Domelevo and P. Omnès in 2D, we consider a ``double'' covering $\Tau$ of a three-dimensional domain by a rather general primal mesh and by a well-chosen ``dual'' mesh. The associated discrete divergence operator $\div^{\ptTau}$ is obtained by the standard finite volume approach. A simple and consistent discrete gradient operator $\grad^\ptTau$ is defined by local affine interpolation that takes into account the geometry of the double mesh. Under mild geometrical constraints on the choice of the dual volumes, we show that $-\div^{\ptTau}$, $\grad^\ptTau$ are linked by the ``discrete duality property'', which is an analogue of the integration-by-parts formula. The primal mesh need not be conformal, and its interfaces can be general polygons. We give several numerical examples for anisotropic linear diffusion problems; good convergence properties are observed. The sequel [3] of this paper will summarize some key discrete functional analysis tools for DDFV schemes and give applications to proving convergence of DDFV schemes for several nonlinear degenerate parabolic PDEs. | |
| dc.language.iso | en | |
| dc.publisher | Oxford University Press (OUP) | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.subject.en | Non-conformal mesh | |
| dc.subject.en | General mesh | |
| dc.subject.en | Consistency | |
| dc.subject.en | Anisotropic elliptic problems | |
| dc.subject.en | Finite volume approximation | |
| dc.subject.en | Gradient reconstruction | |
| dc.subject.en | Discrete gradient | |
| dc.subject.en | Discrete duality | |
| dc.subject.en | 3D CeVe-DDFV | |
| dc.title.en | On 3D DDFV discretization of gradient and divergence operators. I. Meshing, operators and discrete duality. | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1093/imanum/drr046 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | IMA Journal of Numerical Analysis | |
| bordeaux.page | pp.1574-1603 | |
| bordeaux.volume | 32 | |
| 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-00355212 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00355212v1 | |
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