Discontinuous Galerkin Method for Solving the Shallow Water Equations

The shallow water equations (SWE) are derived from the incompressible Navier-Stokes equations using the hydrostatic assumption and the Boussinesq approximation. The SWE are a system of coupled nonlinear partial differential equations defined on complex physical domains arising, for example, from irregular land boundaries. The discontinuous Galerkin methdos (DG methods) is are a from of methods for solving partial differential equations. The combine features of the continuous framework and have been succesfully appled to problems  arising from a wider range of applications. In this project, we formulate the discontinuous Galerkin methods (DG methods) for solving the shallow water equations (SWE) and study them using methods of numerical analysis