Super-convergence of Discontinuous Galerkin Method Applied to the Navier-Stokes Equations

The practical benefits of the hyper-accuracy properties of the discontinuous Galerkin method are examined. In particular, we demonstrate that some flow attributes exhibit super-convergence even in the absence of any post-procesing technique. Theoretical analysis suggest that flow features that are dominated by global propogation speeds and decay or growth rates should be super-convergent. Several discrete forms of the discontinuous Galerkin method are applied to the simulation of unsteady viscous flow over a twodimensional cylinder. Convergence of the period of the naturally occurring oscillation is examined and shown to converge at 2p+1, where p is the polynomial degree of the discontinuous Galerkin basis. Comparisons are made between the different discretizations and with theoretical analysis.