Two-dimensional dispersion analyses of nite element approximations to the shallow water equations

Dispersion analysis of discrete solutions to the shallow water equations has been extensively used as a tool to de ne the relationships between frequency and wave number and to determine if an algorithm leads to a dual wave number response and near 2 x oscillations. In this paper, we explore the application of two-dimensional dispersion analysis to cluster based and Galerkin nite element-based discretizations of the primitive shallow water equations and the generalized wave continuity equation (GWCE) reformulation of the harmonic shallow water equations on a number of grid con gurations. It is demonstrated that for various algorithms and grid con gurations, contradictions exist between the results of one-dimensional and two-dimensional dispersion analysis as a result of subtle changes in the mass matrix. Numerical experiments indicate that the two-dimensional dispersion analysis correctly predicts the existence and onset of near 2 x noise in the solution. Copyright ? 2004 John Wiley & Sons, Ltd.