Hypocoercivity and diffusion limit of a ...
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
Auteur(s) :
Bessemoulin-Chatard, Marianne [Auteur]
Laboratoire de Mathématiques Jean Leray [LMJL]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rey, Thomas [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire de Mathématiques Jean Leray [LMJL]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Rey, Thomas [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI ]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Titre de la revue :
Mathematics of Computation
Pagination :
1093-1133
Éditeur :
American Mathematical Society
Date de publication :
2020-01
ISSN :
0025-5718
Mot(s)-clé(s) en anglais :
kinetic equations
hypocoercivity
finite volume methods
diffusion limit
Asymptic preserving schemes
hypocoercivity
finite volume methods
diffusion limit
Asymptic preserving schemes
Discipline(s) HAL :
Mathématiques [math]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Analyse numérique [math.NA]
Résumé en anglais : [en]
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate ...
Lire la suite >In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates, we establish that the proposed scheme is Asymptotic-Preserving in the diffusive limit. Moreover, we adapt to the discrete framework the hypocoercivity method proposed by [J. Dolbeault, C. Mouhot and C. Schmeiser, Trans. Amer. Math. Soc., 367, 6 (2015)] to prove the exponential return to equilibrium of the approximate solution. We obtain decay rates that are bounded uniformly in the diffusive limit.Finally, we present an efficient implementation of the proposed numerical schemes, and perform numerous numerical simulations assessing their accuracy and efficiency in capturing the correct asymptotic behaviors of the models.Lire moins >
Lire la suite >In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates, we establish that the proposed scheme is Asymptotic-Preserving in the diffusive limit. Moreover, we adapt to the discrete framework the hypocoercivity method proposed by [J. Dolbeault, C. Mouhot and C. Schmeiser, Trans. Amer. Math. Soc., 367, 6 (2015)] to prove the exponential return to equilibrium of the approximate solution. We obtain decay rates that are bounded uniformly in the diffusive limit.Finally, we present an efficient implementation of the proposed numerical schemes, and perform numerous numerical simulations assessing their accuracy and efficiency in capturing the correct asymptotic behaviors of the models.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Projet ANR :
Commentaire :
39 pages
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