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

Bernardo Cockburn, Guido Kanschat, Dominik Schötzau

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)188-210
Number of pages23
JournalJournal of Scientific Computing
Volume40
Issue number1-3
DOIs
StatePublished - Dec 20 2008
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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