The discontinuous Galerkin method with LaxWendroff type time discretizations
In this paper we develop a LaxWendroff time discretization procedure for the discontinuous Galerkin method (LWDG) to solve hyperbolic conservation laws. This is an alternative method for time discretization to the popular total variation diminishing (TVD) RungeKutta time discretizations. The LWDG is a one step, explicit, high order finite element method. The limiter is performed once every time step. As a result, LWDG is more compact than RungeKutta discontinuous Galerkin (RKDG) and the LaxWendroff time discretization procedure is more cost effective than the RungeKutta time discretizations for certain problems including two-dimensional Euler systems of compressible gas dynamics when nonlinear limiters are applied.
discontinuous galerkin method laxwendroff type time discretization limiter rungekutta method weno scheme high order accuracy