An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

Handle URI:
http://hdl.handle.net/10754/597522
Title:
An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
Authors:
Cockburn, Bernardo; Kanschat, Guido; Schötzau, Dominik
Abstract:
We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.
Citation:
Cockburn B, Kanschat G, Schötzau D (2008) An Equal-Order DG Method for the Incompressible Navier-Stokes Equations. Journal of Scientific Computing 40: 188–210. Available: http://dx.doi.org/10.1007/s10915-008-9261-1.
Publisher:
Springer Nature
Journal:
Journal of Scientific Computing
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
20-Dec-2008
DOI:
10.1007/s10915-008-9261-1
Type:
Article
ISSN:
0885-7474; 1573-7691
Sponsors:
G. Kanschat was supported in part by NSF through award no. DMS-0713829 and by awardno. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).D. Schötzau was supported in part by the Natural Sciences and Engineering Research Council ofCanada (NSERC).
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Full metadata record

DC FieldValue Language
dc.contributor.authorCockburn, Bernardoen
dc.contributor.authorKanschat, Guidoen
dc.contributor.authorSchötzau, Dominiken
dc.date.accessioned2016-02-25T12:41:22Zen
dc.date.available2016-02-25T12:41:22Zen
dc.date.issued2008-12-20en
dc.identifier.citationCockburn B, Kanschat G, Schötzau D (2008) An Equal-Order DG Method for the Incompressible Navier-Stokes Equations. Journal of Scientific Computing 40: 188–210. Available: http://dx.doi.org/10.1007/s10915-008-9261-1.en
dc.identifier.issn0885-7474en
dc.identifier.issn1573-7691en
dc.identifier.doi10.1007/s10915-008-9261-1en
dc.identifier.urihttp://hdl.handle.net/10754/597522en
dc.description.abstractWe introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.en
dc.description.sponsorshipG. Kanschat was supported in part by NSF through award no. DMS-0713829 and by awardno. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).D. Schötzau was supported in part by the Natural Sciences and Engineering Research Council ofCanada (NSERC).en
dc.publisherSpringer Natureen
dc.subjectDiscontinuous Galerkin methodsen
dc.subjectEqual-order methodsen
dc.subjectIncompressible Navier-Stokes equationsen
dc.titleAn Equal-Order DG Method for the Incompressible Navier-Stokes Equationsen
dc.typeArticleen
dc.identifier.journalJournal of Scientific Computingen
dc.contributor.institutionUniversity of Minnesota Twin Cities, Minneapolis, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionThe University of British Columbia, Vancouver, Canadaen
kaust.grant.numberKUS-C1-016-04en
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