Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations Original Research Article

In this paper, we investigate a new approach for the two-dimensional fully non-linear depth-averaged shallow water equations by coupling continuous and discontinuous Galerkin methods. We apply a discontinuous Galerkin method to the primitive continuity and momentum equations and couple this to a continuous method discretizing the so-called “wave continuity” and momentum equation. Herein we present the formulation and derive an a priori error estimate, and demonstrate some preliminary numerical results. This work represents the culmination of a series of papers exploring coupled methods for the shallow water equations.