Incompressible velocity approximations for incompressible fluid flow using DG methods
Mathematics Department, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
ABSTRACT
We describe a discontinuous Galerkin method for the incompressible stationary Navier-Stokes equations whose main feature is that it provides a globally divergence-free approximate velocity. This is achieved by a suitable use of a simple, element-by-element post-processing of the completely discontinuous approximations typical of these types of methods. Optimal error estimates are proved and an efficient iterative procedure to compute the approximate solution is shown to converge. Numerical results are displayed that verify the theoretical rates of convergence.
Keywords:
Discontinuous Galerkin methods; Incompressible fluid flow