Analysis of discontinuous finite element methods for ground water/surface water coupling

We derive and analyze new numerical approaches for modeling coupled ground water/surface water flow. In this coupled model, surface water flow is described by the depth-averaged shallow water equations, while ground water is modeled by saturated Darcy flow. The coupling between the two models assumes continuity of pressure and water flux across the ground water/surface water interface. The coupled model is approximated by a local discontinuous Galerkin method for ground water flow and a discontinuous Galerkin method for surface water flow. A priori error estimates are derived for this approach. A closely related approach where the well-known mixed finite element method is applied to the ground water flow equations is also described and analyzed. One advantage of these approaches is that they allow for the ground water and surface water domains to be meshed independently, under some mild restrictions.