A characteristic-Galerkin approximation to a system of shallow water equations

Characteristic methods are known to handle advective flow better than tradi tional Galerkin methods and allow large time steps to be taken when compare d to standard time-stepping methods. In this paper, we investigate a charac teristic-Galerkin approximation to the 2-dimensional system of shallow wate r equations. We derive L-infinity ((0; T); L-2(Omega)) bounds for elevation and velocity, showing these to be optimal for velocity in L-2 ((0, T); H-1 (Omega)).