Edge-based finite element method for shallow water equations

This paper describes an edge-based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non-linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi-discrete and space-time analyses. Stabilized formulations, including Petrov-Galerkin models and discontinuity-capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge-based approach are presented at the end of the paper. Copyright (C) 2001 John Wiley & Sons, Ltd.