The analogue of grad-div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshes

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dc.contributor.authorAkbaş, Mine
dc.contributor.authorLinke, Alexander
dc.contributor.authorRebholz, Leo G.
dc.contributor.authorSchröder, Philipp W.
dc.date.accessioned2020-04-30T23:32:37Z
dc.date.available2020-04-30T23:32:37Z
dc.date.issued2018
dc.departmentDÜ, Fen-Edebiyat Fakültesi, Matematik Bölümüen_US
dc.descriptionSchroeder, Philipp W./0000-0001-7644-4693en_US
dc.descriptionWOS: 000442638700037en_US
dc.description.abstractgrad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the relaxation of the divergence constraint in classical mixed methods, and are excited whenever the spatial discretization has to deal with comparably large and complicated pressures. In this contribution, an analogue of grad-div stabilization for Discontinuous Galerkin methods is studied. Here, the key is the penalization of the jumps of the normal velocities over facets of the triangulation, which controls the measure-valued part of the distributional divergence of the discrete velocity solution. Our contribution is twofold: first, we characterize the limit for arbitrarily large penalization parameters, which shows that the stabilized nonconforming Discontinuous Galerkin methods remain robust and accurate in this limit; second, we extend these ideas to the case of non-simplicial meshes; here, broken grad-div stabilization must be used in addition to the normal velocity jump penalization, in order to get the desired pressure robustness effect. The analysis is performed for the Stokes equations, and more complex flows and Crouzeix-Raviart elements are considered in numerical examples that also show the relevance of the theory in practical settings. (C) 2018 Elsevier B.V. All rights reserved.en_US
dc.description.sponsorshipGerman Academic Exchange Service (DAAD)Deutscher Akademischer Austausch Dienst (DAAD); program "Research Grants for Doctoral Candidates and Young Academics and Scientists", 2017/18 [57299291]; National Science FoundationNational Science Foundation (NSF) [DMS1522191]; U.S. ArmyUnited States Department of Defense [65294-MA]en_US
dc.description.sponsorshipThe authors would especially like to thank Christoph Lehrenfeld for several related fruitful discussions on stabilization and hybridization and the invaluable help he provided in using the finite element library NGSolve in the context of this work. Mine Akbas acknowledges support from the German Academic Exchange Service (DAAD) with the program "Research Grants for Doctoral Candidates and Young Academics and Scientists", 2017/18 (57299291). The third author was supported by National Science Foundation grant DMS1522191 and U.S. Army grant 65294-MA.en_US
dc.identifier.doi10.1016/j.cma.2018.07.019en_US
dc.identifier.endpage938en_US
dc.identifier.issn0045-7825
dc.identifier.issn1879-2138
dc.identifier.scopusqualityQ1en_US
dc.identifier.startpage917en_US
dc.identifier.urihttps://doi.org/10.1016/j.cma.2018.07.019
dc.identifier.urihttps://hdl.handle.net/20.500.12684/4771
dc.identifier.volume341en_US
dc.identifier.wosWOS:000442638700037en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevier Science Saen_US
dc.relation.ispartofComputer Methods In Applied Mechanics And Engineeringen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectIncompressible Navier-Stokes equationsen_US
dc.subjectMixed finite element methodsen_US
dc.subjectgrad-div stabilizationen_US
dc.subjectDiscontinuous Galerkin methoden_US
dc.subjectNonconforming finite elementsen_US
dc.titleThe analogue of grad-div stabilization in DG methods for incompressible flows: Limiting behavior and extension to tensor-product meshesen_US
dc.typeArticleen_US

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