Discontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water Original Research Article

In this paper, we investigate a new approach for the numerical solution of the two-dimensional depth-integrated shallow water equations, based on coupling discontinuous and continuous Galerkin methods. In this approach, we couple a discontinuous Galerkin method applied to the primitive continuity equation, coupled to a continuous Galerkin method applied to the so-called “wave continuity equation.” The formulation is derived and a priori error estimates are given. Preliminary numerical results for a simple model of flow in a channel are presented.