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

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 [15].

• Type: Journal
• Year: 2007
• Where: JSCIC
• Authors: Bernardo Cockburn, Guido Kanschat, Dominik Schötzau
• Keywords: Discontinuous Galerkin Methods, Divergence-conforming Velocity, Incompressible Navier-stokes Equations, JSCIC 2007