Show simple item record

hal.structure.identifierLaboratoire Paul Painlevé - UMR 8524 [LPP]
dc.contributor.authorCancès, Clément
HAL ID: 171
ORCID: 0000-0002-7682-1695
*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorGallouët, Thomas
HAL ID: 3710
*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorTodeschi, Gabriele*
dc.date.accessioned2019-10-16T13:53:21Z
dc.date.available2019-10-16T13:53:21Z
dc.date.issued2020
dc.identifier.issn0029-599X
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20187
dc.language.isoenen
dc.subjectWasserstein gradient flows
dc.subjectBenamou-Brenier formula
dc.subject.ddc515en
dc.titleA variational finite volume scheme for Wasserstein gradient flows
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula, whereas space discretization relies on upstream mobility two-point flux approximation finite volumes. Our scheme is based on a first discretize then optimize approach in order to preserve the variational structure of the continuous model at the discrete level. Our scheme can be applied to a wide range of energies, guarantees non-negativity of the discrete solutions as well as decay of the energy. We show that our scheme admits a unique solution whatever the convex energy involved in the continuous problem , and we prove its convergence in the case of the linear Fokker-Planck equation with positive initial density. Numerical illustrations show that it is first order accurate in both time and space, and robust with respect to both the energy and the initial profile.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameNumerische Mathematik
dc.relation.isversionofjnldate2020
dc.relation.isversionofjnlpages34
dc.relation.isversionofdoi10.1007/s00211-020-01153-9
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-10-30T13:35:01Z
hal.author.functionaut
hal.author.functionaut
hal.author.functionaut


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record