A new triangular finite-element with optimum constraint ratio for compressible fluids

The discretization of the shallow-water equations using the finite-element method is a delicate problem. Apart from the possible occurrence of pressur e and/or velocity modes, other spurious modes may appear that are essential ly a consequence of having more momentum than continuity discretized equati ons, contrary to the continuum case. In this paper a new triangular finite- element pair is proposed which overcomes this imbalance problem. The new pa ir is shown to improve on results obtained with existing pairs in represent ing the propagation of fast gravity and slow Rossby waves by discretizing t he linear shallow-water equations.