An equal-order DG method for the incompressible navier-stokes equations

Bernardo Cockburn, Guido Kanschat, Dominik Schötzau

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46 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)188-210
Number of pages23
JournalJournal of Scientific Computing
Issue number1-3
StatePublished - Jul 2009

Bibliographical note

Funding Information:
B. Cockburn was supported in part by the National Science Foundation (Grant DMS-0712955) and by the University of Minnesota Supercomputing Institute. G. Kanschat was supported in part by NSF through award no. DMS-0713829 and by award no. 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 of Canada (NSERC).


  • Discontinuous Galerkin methods
  • Equal-order methods
  • Incompressible Navier-Stokes equations


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