A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2740
dc.contributor.authorAhmed, Naveed
dc.contributor.authorBarrenechea, Gabriel R.
dc.contributor.authorBurman, Erik
dc.contributor.authorGuzmán, Johnny
dc.contributor.authorLinke, Alexander
dc.contributor.authorMerdon, Christian
dc.date.accessioned2022-06-30T13:03:32Z
dc.date.available2022-06-30T13:03:32Z
dc.date.issued2020
dc.description.abstractDiscretization of Navier--Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressureindependent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(hk+1/2) error estimate in the L2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.eng
dc.description.versionpublishedVersioneng
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/9390
dc.identifier.urihttps://doi.org/10.34657/8428
dc.language.isoeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
dc.relation.doihttps://doi.org/10.20347/WIAS.PREPRINT.2740
dc.relation.hasversionhttps://doi.org/10.1137/20M1351230
dc.relation.issn2198-5855
dc.rights.licenseThis 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.licenseDieses 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.subjectincompressible Navier--Stokes equationseng
dc.subjectdivergence-free mixed finite element methodseng
dc.subjectpressure-robustnesseng
dc.subjectconvection stabilizationeng
dc.subjectGalerkin least squareseng
dc.subjectvorticity equationeng
dc.subject.ddc510
dc.titleA pressure-robust discretization of Oseen's equation using stabilization in the vorticity equationeng
dc.typereporteng
dc.typeTexteng
dcterms.extent34 S.
tib.accessRightsopenAccess
wgl.contributorWIAS
wgl.subjectMathematik
wgl.typeReport / Forschungsbericht / Arbeitspapier
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