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.
Bibliographical noteFunding 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: email@example.com 2Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120 Heidelberg, Germany. E-mail: firstname.lastname@example.org 3Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada. E-mail: email@example.com 4To whom correspondence should be addressed. firstname.lastname@example.org
- Discontinuous Galerkin methods
- Divergence-free condition
- Navier-Stokes equations