An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods

In this paper, we present a discontinuous Galerkin formulation of the shallow-water equations. An orthogonal basis is used for the spatial discretization and an explicit Runge-Kutta scheme is used for time discretization. Some results of second-order anisotropic adaptive calculations are presented for dam breaking problems. The adaptive procedure uses an error indicator that concentrates the computational effort near discontinuities like hydraulic jumps.