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dc.contributor.authorBonilla de Toro, Jesús
dc.contributor.authorBadia, Santiago
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.date.accessioned2019-06-18T07:25:16Z
dc.date.available2021-06-04T00:26:59Z
dc.date.issued2019-09
dc.identifier.citationBonilla, J.; Badia, S. Maximum-principle preserving space–time isogeometric analysis. "Computer methods in applied mechanics and engineering", Setembre 2019, vol. 354, p. 422-440.
dc.identifier.issn0045-7825
dc.identifier.otherhttps://arxiv.org/abs/1812.05442
dc.identifier.urihttp://hdl.handle.net/2117/134634
dc.description.abstractIn this work we propose a nonlinear stabilization technique for convection–diffusion–reaction and pure transport problems discretized with space–time isogeometric analysis. The stabilization is based on a graph-theoretic artificial diffusion operator and a novel shock detector for isogeometric analysis. Stabilization in time and space directions are performed similarly, which allow us to use high-order discretizations in time without any CFL-like condition. The method is proven to yield solutions that satisfy the discrete maximum principle (DMP) unconditionally for arbitrary order. In addition, the stabilization is linearity preserving in a space–time sense. Moreover, the scheme is proven to be Lipschitz continuous ensuring that the nonlinear problem is well-posed. Solving large problems using a space–time discretization can become highly costly. Therefore, we also propose a partitioned space–time scheme that allows us to select the length of every time slab, and solve sequentially for every subdomain. As a result, the computational cost is reduced while the stability and convergence properties of the scheme remain unaltered. In addition, we propose a twice differentiable version of the stabilization scheme, which enjoys the same stability properties while the nonlinear convergence is significantly improved. Finally, the proposed schemes are assessed with numerical experiments. In particular, we considered steady and transient pure convection and convection–diffusion problems in one and two dimensions.
dc.format.extent19 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional
dc.subject.lcshIsogeometric analysis
dc.subject.lcshFinite element method
dc.subject.otherIsogeometric analysis
dc.subject.otherDiscrete maximum principle
dc.subject.otherMonotonicity
dc.subject.otherHigh-order
dc.subject.otherSpace–time
dc.titleMaximum-principle preserving space–time isogeometric analysis
dc.typeArticle
dc.subject.lemacMecànica computacional
dc.subject.lemacElements finits, Mètode dels
dc.contributor.groupUniversitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica
dc.identifier.doi10.1016/j.cma.2019.05.042
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0045782519303123
dc.rights.accessOpen Access
local.identifier.drac25190731
dc.description.versionPostprint (author's final draft)
local.citation.authorBonilla, J.; Badia, S.
local.citation.publicationNameComputer methods in applied mechanics and engineering
local.citation.volume354
local.citation.startingPage422
local.citation.endingPage440


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