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hal.structure.identifierReliable numerical approximations of dissipative systems [RAPSODI ]
dc.contributor.authorNatale, Andrea
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorTodeschi, Gabriele
dc.date.accessioned2021-11-25T10:24:53Z
dc.date.available2021-11-25T10:24:53Z
dc.date.issued2021
dc.identifier.issn1290-3841
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22242
dc.language.isoenen
dc.subjectFinite volumesen
dc.subjectDynamical optimal transporten
dc.subjectBarrier methoden
dc.subject.ddc515en
dc.titleComputation of optimal transport with finite volumesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe construct Two-Point Flux Approximation (TPFA) finite volume schemes to solve the quadratic optimal transport problem in its dynamic form, namely the problem originally introduced by Benamou and Brenier. We show numerically that these type of discretizations are prone to form instabilities in their more natural implementation, and we propose a variation based on nested meshes in order to overcome these issues. Despite the lack of strict convexity of the problem, we also derive quantitative estimates on the convergence of the method, at least for the discrete potential and the discrete cost. Finally, we introduce a strategy based on the barrier method to solve the discrete optimization problem.en
dc.relation.isversionofjnlnameESAIM: Mathematical Modelling and Numerical Analysis
dc.relation.isversionofjnlvol55en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2021
dc.relation.isversionofjnlpages1847-1871en
dc.relation.isversionofdoi10.1051/m2an/2021041en
dc.relation.isversionofjnlpublisherEDP Sciencesen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-25T10:21:48Z
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