Abstract
The frequency or dispersion relation for the discontinuous Galerkin mixed formulation of the 1-D linearized shallow-water equations is analysed, using several basic DG mixed schemes. The dispersion properties are compared analytically and graphically with those of the mixed continuous Galerkin formulation for piecewise-linear bases on co-located grids. Unlike the Galerkin case, the DG scheme does not exhibit spurious stationary pressure modes. However, spurious propagating modes have been identified in all the present discontinuous Galerkin formulations. Numerical solutions of a test problem to simulate fast gravity modes illustrate the theoretical results and confirm the presence of spurious propagating modes in the DG schemes. Copyright © 2005 John Wiley & Sons, Ltd.
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