A COMPARISON OF THE DISPERSION AND DISSIPATION ERRORS OF GAUSS AND GAUSS-LOBATTO DISCONTINUOUS GALERKIN SPECTRAL ELEMENT METHODS

We examine the dispersion and dissipation properties of the Gauss and Gauss-Lobatto discontinuous Galerkin spectral element methods (DGSEMs), for linear wave propagation problems. We show that the inherent underintegration in the Gauss-Lobatto variant can be interpreted as a modal filtering of the highest polynomial mode. This in turn has a drastic impact on the dispersion and dissipation relations of the Gauss-Lobatto DGSEM compared to the Gauss variant. We show that the Gauss DGSEM is typically more accurate than the Gauss-Lobatto variant, needing fewer points per wavelength for a given accuracy while on the other hand being more restricted in the explicit time step choice. We show that the spectra of the DGSEM operators depend on the boundary conditions applied and that the ratio of the time step restrictions of the two schemes depends on the choice of boundary conditions.