Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 31, Issue 1-2, Pages 61-73Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-006-9107-7
Keywords
Navier-Stokes equations; divergence-free condition; discontinuous Galerkin methods
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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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