dc.contributor.author Cusimano, N. dc.contributor.author Del Teso, F. dc.contributor.author Gerardo-Giorda, L. dc.contributor.author Pagnini, G. dc.date.accessioned 2017-08-07T06:38:16Z dc.date.available 2017-08-07T06:38:16Z dc.date.issued 2017-04-28 dc.identifier.issn 1095-7170 dc.identifier.uri http://hdl.handle.net/20.500.11824/718 dc.description.abstract In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable quadrature formulas of the integral with a finite element method for the approximation of the solution of the corresponding heat equation. We derive two families of discretisations with order of convergence depending on the regularity of the domain and the function on which the fractional Laplacian is acting. Unlike other existing approaches in literature, our method does not require the computation of the eigenpairs of the Laplacian on the considered domain, can be implemented on possibly irregular bounded domains, and can naturally handle different types of boundary constraints. Various numerical simulations are provided to illustrate performance of the proposed method and support our theoretical results. en_US dc.description.sponsorship FdT acknowledges support of en_US Toppforsk project Waves and Nonlinear Phenomena (WaNP), grant no. 250070 from the Research Council of Norway. ERCIM Alain Benoussan" Fellowship programme dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Fractional Laplacian en_US dc.subject Bounded Domain en_US dc.subject Homogeneous and Nonhomogeneous Boundary Conditions en_US dc.subject Heat-Semigroup Formulation en_US dc.subject Finite elements en_US dc.subject Integral Quadrature en_US dc.title Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions en_US dc.type info:eu-repo/semantics/conferenceObject en_US dc.identifier.doi 10.1137/17M1128010 dc.relation.publisherversion https://epubs.siam.org/doi/10.1137/17M1128010 dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID ES/1PE/MTM2016-76016-R en_US dc.relation.projectID ES/1PE/MTM2015-69992-R en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US
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