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dc.contributor.authorDuprez, Michel*
dc.contributor.authorLozinski, Alexei*
dc.date.accessioned2020-04-29T11:32:12Z
dc.date.available2020-04-29T11:32:12Z
dc.date.issued2020
dc.identifier.issn0036-1429
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20676
dc.language.isoenen
dc.subjectFinite element method
dc.subjectfictitious domain
dc.subjectlevel-set
dc.subject.ddc515en
dc.titleφ-FEM: a finite element method on domains defined by level-sets
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe propose a new fictitious domain finite element method, well suited for elliptic problems posed in a domain given by a level-set function without requiring a mesh fitting the boundary. To impose the Dirichlet boundary conditions, we search the approximation to the solution as a product of a finite element function with the given level-set function, which is also approximated by finite elements. Unlike other recent fictitious domain-type methods (XFEM, CutFEM), our approach does not need any non-standard numerical integration (on cut mesh elements or on the actual boundary). We consider the Poisson equation discretized with piecewise polynomial Lagrange finite elements of any order and prove the optimal convergence of our method in the H1-norm. Moreover, the discrete problem is proven to be well conditioned, i.e. the condition number of the associated finite element matrix is of the same order as that of a standard finite element method on a comparable conforming mesh. Numerical results confirm the optimal convergence in both H1 and L2 norms.
dc.relation.isversionofjnlnameSIAM Journal on Numerical Analysis
dc.relation.isversionofjnlvol58
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2020
dc.relation.isversionofdoi10.1137/19M1248947
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-06-12T09:52:13Z
hal.person.labIds60*
hal.person.labIds45*


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