A Local Discontinuous Petrov-Galerkin Method For Partial Differential Equations With Higher Order Derivatives

In this paper,a method for solving partial differential equations with high order derivative is discussed.First the local discontinuous Petrov-Galerkin method(LDPG)is used for spatial discretization.This method can deal with discontinuous solutions and complex boundary conditions well and has natural local conservation.Then,third order TVD Runge-Kutta method is used for time discretization.In addition,we perform Fourier analysis on the linear diffusion equation,the linear dispersion equation and the linear convection dispersion equation.And also give the numerical examples in order to proved the stability of the above equations under the LDPG scheme.At the end of the paper,several typical examples of partial equations with high order derivative are given.To verify the reliability of the LDPG scheme,we simulate the motion trajectory of the compactons at different times.