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

Type
Article

Authors
Cockburn, Bernardo
Kanschat, Guido
Schötzau, Dominik

KAUST Grant Number
KUS-C1-016-04

Online Publication Date
2008-12-20

Print Publication Date
2009-07

Date
2008-12-20

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.

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).

Publisher
Springer Nature

Journal
Journal of Scientific Computing

DOI
10.1007/s10915-008-9261-1

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