An Equal-Order DG Method for the Incompressible Navier-Stokes Equations
KAUST Grant NumberKUS-C1-016-04
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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.
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.
SponsorsG. 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).
JournalJournal of Scientific Computing