Divergence-free reconstruction operators for pressure-robust Stokes discretizations with continuous pressure finite elements
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2288 | |
dc.contributor.author | Lederer, Philip L. | |
dc.contributor.author | Linke, Alexander | |
dc.contributor.author | Merdon, Christian | |
dc.contributor.author | Schöberl, Joachim | |
dc.date.accessioned | 2016-12-14T22:47:00Z | |
dc.date.available | 2019-06-28T08:11:48Z | |
dc.date.issued | 2016 | |
dc.description.abstract | Classical inf-sup stable mixed finite elements for the incompressible (Navier-)Stokes equations are not pressure-robust, i.e., their velocity errors depend on the continuous pressure. However, a modification only in the right hand side of a Stokes discretization is able to reestablish pressure-robustness, as shown recently for several inf-sup stable Stokes elements with discontinuous discrete pressures. In this contribution, this idea is extended to low and high order Taylor-Hood and mini elements, which have continuous discrete pressures. For the modification of the right hand side a velocity reconstruction operator is constructed that maps discretely divergence-free test functions to exactly divergence-free ones. The reconstruction is based on local H (div)-conforming flux equilibration on vertex patches, and fulfills certain orthogonality properties to provide consistency and optimal a-priori error estimates. Numerical examples for the incompressible Stokes and Navier-Stokes equations confirm that the new pressure-robust Taylor-Hood and mini elements converge with optimal order and outperform significantly the classical versions of those elements when the continuous pressure is comparably large. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/2246 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2830 | |
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 | pressure robustness | eng |
dc.subject.other | exact divergence-free velocity reconstruction | eng |
dc.subject.other | flux equilibration | eng |
dc.title | Divergence-free reconstruction operators for pressure-robust Stokes discretizations with continuous pressure finite 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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