Dispersion analysis of the least-squares finite-element shallow-water system

The frequency or dispersion relation for the least-squares mixed formulation of the shallow-water equations is analysed. We consider the use of different approximation spaces corresponding to co-located and staggered meshes, respectively. The study includes the effect of Coriolis, and the dispersion properties are compared analytically and graphically with those of the mixed Galerkin formulation. Numerical solutions of a test problem to simulate slow Rossby modes illustrate the theoretical results.