Discontinuous and coupled continuous/discontinuous Galerkin methods for the shallow water equations

We consider the approximation of a simplified model of the depth-averaged two-dimensional shallow water equations by two approaches. In both approaches. a discontinuous Galerkin (DG) method is used to approximate the continuity equation. In the first approach, a continuous Galerkin method is used for the momentum equations. In the second approach a particular DG method, the nonsymmetric interior penalty Galerkin method, is used to approximate momentum. A priori error estimates are derived and numerical results are presented for both approaches. (C) 2002 Elsevier Science B.V. All rights reserved.