The Discontinuous Galerkin Method For Regularized Long Wave Equation

In this paper,the regularized long wave?RLW?equation of discontinuous galerkin?DG?method is investigated.To the one-dimensional RLW equation,time discretization is using Runge-Kutta method and Crank-Nicolson method,respective-ly.To the two-dimensional RLW equation,time discretization is using Runge-Kutta method.It is proved that the semi-discrete scheme of the RLW equation preserves two conserved quantities under periodic boundary conditions.And the numerical results show that the DG scheme with suitable numerical flux maintain the conser-vation of₁,₂and₃under periodic boundary conditions.For⁶)element,the scheme has6)+1 order accuracy,it is further shown that the numerical scheme can be more stable by choosing appropriate numerical flux through numerical experiments.