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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierInria Bordeaux - Sud-Ouest
hal.structure.identifierModélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
dc.contributor.authorBENDAHMANE, Mostafa
hal.structure.identifierUniversité Libanaise, Ecole Doctorale des Sciences et de Technologie
dc.contributor.authorMROUÉ, Fatima
hal.structure.identifierÉcole Centrale de Nantes [ECN]
dc.contributor.authorSAAD, Mazen
dc.date.accessioned2024-04-04T02:42:45Z
dc.date.available2024-04-04T02:42:45Z
dc.date.issued2021-01
dc.identifier.issn0749-159X
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191272
dc.description.abstractEnThe monodomain model is a widely used model in electrocardiology to simulate the propagation of electrical potential in the myocardium. In this paper, we investigate a positive nonlinear control volume finite element (CVFE) scheme, based on Godunov's flux approximation of the diffusion term, for the monodomain model coupled to a physiological ionic model (the Beeler-Reuter model) and using an anisotropic diffusion tensor. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in conforming finite element methods. The diffusion term which involves an anisotropic tensor is discretized on a dual mesh using the diffusion fluxes provided by the conforming finite element reconstruction on the primal mesh and the other terms are discretized by means of an upwind finite volume method on the dual mesh. The scheme ensures the validity of the discrete maximum principle without any restriction on the transmissibility coefficients. By using a compactness argument, we obtain the convergence of the discrete solution and as a consequence, we get the existence of a weak solution of the original model. Finally, we illustrate the efficiency of the proposed scheme by exhibiting some numerical results.
dc.language.isoen
dc.publisherWiley
dc.subject.enMonodomain model
dc.subject.enFinite volume
dc.subject.enFinite Element
dc.subject.enGodunov Scheme
dc.subject.enMaximum principle
dc.subject.enConvergence
dc.title.enA positive cell vertex godunov scheme for a beeler-reuter based model of cardiac electrical activity
dc.typeArticle de revue
dc.identifier.doi10.1002/num.22528
dc.subject.halMathématiques [math]
dc.subject.halSciences du Vivant [q-bio]
bordeaux.journalNumerical Methods for Partial Differential Equations
bordeaux.page262-301
bordeaux.volume37
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03534773
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03534773v1
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