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A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120, Heidelberg, Germany

    Guido Kanschat

  3. Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Dominik Schötzau

Authors
  1. Bernardo Cockburn
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  2. Guido Kanschat
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  3. Dominik Schötzau
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Corresponding author

Correspondence to Bernardo Cockburn.

Additional information

Bernardo Cockburn, supported in part by NSF Grant DMS-0411254.

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Cockburn, B., Kanschat, G. & Schötzau, D. A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations. J Sci Comput 31, 61–73 (2007). https://doi.org/10.1007/s10915-006-9107-7

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  • DOI: https://doi.org/10.1007/s10915-006-9107-7

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