Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations
| 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 | Center of Mathematics for Applications [Oslo] [CMA] | |
| dc.contributor.author | KARLSEN, Kenneth Hvistendahl | |
| dc.date.accessioned | 2024-04-04T02:29:08Z | |
| dc.date.available | 2024-04-04T02:29:08Z | |
| dc.date.issued | 2010 | |
| dc.identifier.issn | 0219-8916 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190150 | |
| dc.description.abstractEn | We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the construction and analysis of discrete duality finite volume schemes (in the spirit of Domelevo and Omn`es [43]) for these problems in two and three spatial dimensions. We derive a series of discrete duality formulas and entropy dissipation inequalities for the schemes. We establish the existence of solutions to the discrete problems, and prove that sequences of approximate solutions generated by the discrete duality finite volume schemes converge strongly to the entropy solution of the continuous problem. The proof revolves around basic a priori estimates, the discrete duality features, Minty–Browder type arguments, and “hyperbolic” L∞ weak-* compactness arguments (i.e. propagation of compactness along the lines of Tartar, DiPerna, . . . ). Our results cover the case of non-Lipschitz nonlinearities. | |
| dc.language.iso | en | |
| dc.publisher | World Scientific Publishing | |
| dc.subject | convergence | |
| dc.subject.en | Degenerate hyperbolic-parabolic equation | |
| dc.subject.en | conservation law | |
| dc.subject.en | Leray–Lions type operator | |
| dc.subject.en | non-Lipschitz flux | |
| dc.subject.en | entropy solution | |
| dc.subject.en | existence | |
| dc.subject.en | uniqueness | |
| dc.subject.en | finite volume scheme | |
| dc.subject.en | discrete duality | |
| dc.subject.en | convergence. | |
| dc.title.en | Discrete duality finite volume schemes for doubly nonlinear degenerate hyperbolic-parabolic equations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1142/S0219891610002062 | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 0901.0816 | |
| bordeaux.journal | Journal of Hyperbolic Differential Equations | |
| bordeaux.page | 1--67 | |
| bordeaux.volume | 7 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00475752 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00475752v1 | |
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