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

Summary. Characteristic methods are known to handle advective flow better than traditional Galerkin methods and allow large time steps to be taken when compared to standard time-stepping methods. In this paper, we investigate a characteristic-Galerkin approximation to the 2-dimensional system of shallow water equations. We derive ${\cal L}^{\infty}\left ((0,T);{\cal L}^2(\Omega)\right )$ bounds for elevation and velocity, showing these to be optimal for velocity in ${\cal L}^2\left ((0,T);{\cal H}^1(\Omega)\right )$.