Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations
dc.bibliographicCitation.volume | 2250 | |
dc.contributor.author | Linke, Alexander | |
dc.contributor.author | Merdon, Christian | |
dc.date.accessioned | 2016-12-13T10:46:58Z | |
dc.date.available | 2019-06-28T08:01:58Z | |
dc.date.issued | 2016 | |
dc.description.abstract | Recently, it was understood how to repair a certain L2-orthogonality of discretely-divergence-free vector fields and gradient fields such that the velocity error of inf-sup stable discretizations for the incompressible Stokes equations becomes pressure-independent. These new pressure-robust Stokes discretizations deliver a small velocity error, whenever the continuous velocity field can be well approximated on a given grid. On the contrary, classical inf-sup stable Stokes discretizations can guarantee a small velocity error only, when both the velocity and the pressure field can be approximated well, simultaneously. In this contribution, pressure-robustness is extended to the time-dependent Navier-Stokes equations. In particular, steady and time-dependent potential flows are shown to build an entire class of benchmarks, where pressure-robust discretizations can outperform classical approaches significantly. Speedups will be explained by a new theoretical concept, the discrete Helmholtz projector of an inf-sup stable discretization. Moreover, different discrete nonlinear convection terms are discussed, and skew-symmetric pressure-robust discretizations are proposed. | |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 2198-5855 | |
dc.identifier.uri | https://doi.org/10.34657/3002 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/1649 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2250, ISSN 2198-5855 | 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.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.subject | Incompressible Navier–Stokes | |
dc.subject | mixed finite element methods | |
dc.subject | a-priori error estimates | |
dc.subject | pressure-robustness | |
dc.subject | Helmholtz projector | |
dc.subject | irrotational forces | |
dc.subject.ddc | 510 | |
dc.title | Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations | |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- 870508172.pdf
- Size:
- 441.02 KB
- Format:
- Adobe Portable Document Format
- Description: