Improving mass conservation in FE approximations of the Navier Stokes equations using continuous velocity fields: a connection between grad-div stabilization and Scott-Vogelius elements
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 1510 | |
dc.contributor.author | Case, Michael A. | |
dc.contributor.author | Ervin, V.J. | |
dc.contributor.author | Linke, A. | |
dc.contributor.author | Rebholz, L.G. | |
dc.date.accessioned | 2016-03-24T17:38:36Z | |
dc.date.available | 2019-06-28T08:05:08Z | |
dc.date.issued | 2010 | |
dc.description.abstract | This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. Under mild restrictions, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein the first numerical tests of this element pair for the time dependent Navier-Stokes equations. We also prove that, again under these mild restrictions, the limit of the grad-div stabilized Taylor-Hood solutions to the Navier-Stokes problem converges to the Scott-Vogelius solution as the stabilization parameter tends to infinity. That is, in this setting, we provide theoretical justification that choosing the parameter large does not destroy the solution. A limiting result is also proven for the general case. Numerical tests are provided which verify the theory, and show how both Scott-Vogelius and grad-div stabilized Taylor-Hood (with large stabilization parameter) elements can provide accurate results with excellent mass conservation for Navier-Stokes approximations. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2521 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2273 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.issn | 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | eng |
dc.subject.other | incompressible Navier-Stokes equations | eng |
dc.subject.other | mixed finite elements | eng |
dc.subject.other | stabilized finite elements | eng |
dc.subject.other | grad-div stabilization | eng |
dc.subject.other | Taylor-Hood element | eng |
dc.subject.other | Scott-Vogelius element | eng |
dc.title | Improving mass conservation in FE approximations of the Navier Stokes equations using continuous velocity fields: a connection between grad-div stabilization and Scott-Vogelius elements | eng |
dc.type | Report | eng |
dc.type | Text | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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