Dispersion Analysis of the Continuous and Discontinuous Galerkin Formulations

The dispersion relation of the semi-discrete continuous and discontinuous Galerkin formulations are analysed for the linear advection equation. In the context of an spectral/hp element discretisation on an equispaced mesh the problem can be reduced to a P × P eigenvalue problem where P is the polynomial order. The analytical dispersion relationships for polynomial order up to P = 3 and the numerical values for P = 10 are presented demonstrating similar dispersion properties but show that the discontinuous scheme is more diffusive.