DG FEM for Shallow Water Equations

A discontinuous Galerkin(DG) finite element method is utilized to solve the two-dimensional depth-integrated shallow water equations(SWEs).These hyperbolic equations are derived following the laws of conservation.A weak solution is obtained by integrating the equations over a single element,and approximating the unknown variables by discontinuous polynomials.Because of its local nature of discontinuous FEM,the DG method can easily improve the simulation precision through increasing the polynomial order of approximation.The discontinuous FEM is also 'locally conservative',so it is possible to simulate high velocity gradient through integrating numerical flux.Finally,numerical simulation results on Nei River using discontinuous FEM are presented.