A note on discontinuous galerkin divergence-free solutions of the navier-stokes equations

Bernardo Cockburn, Guido Kanschat, Dominik Schötzau

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126 Scopus citations

Abstract

We present a class of discontinuous Galerkin methods for the incompressible Navier-Stokes equations yielding exactly divergence-free solutions. Exact incompressibility is achieved by using divergence-conforming velocity spaces for the approximation of the velocities. The resulting methods are locally conservative, energy-stable, and optimally convergent. We present a set of numerical tests that confirm these properties. The results of this note naturally expand the work in Cockburn et al. (2005) Math. Comp. 74, 1067-1095.

Original languageEnglish (US)
Pages (from-to)61-73
Number of pages13
JournalJournal of Scientific Computing
Volume31
Issue number1-2
DOIs
StatePublished - Jun 2007

Bibliographical note

Funding Information:
∗Bernardo Cockburn, supported in part by NSF Grant DMS-0411254. 1School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA. E-mail: cockburn@math.umn.edu 2Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120 Heidelberg, Germany. E-mail: kanschat@dgfem.org 3Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. E-mail: schoetzau@math.ubc.ca 4To whom correspondence should be addressed. cockburn@math.umn.edu

Keywords

  • Discontinuous Galerkin methods
  • Divergence-free condition
  • Navier-Stokes equations

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