Numerical solution of the Burgers’ equation by local discontinuous Galerkin method

Abstract

In this paper, the Burgers’ equation is transformed into the linear diffusion equation by using the Hopf–Cole transformation. The obtained linear diffusion equation is discretized in space by the local discontinuous Galerkin method. The temporal discretization is accomplished by the total variation diminishing Runge–Kutta method. Numerical solutions are compared with the exact solution and the numerical solutions obtained by Adomian’s decomposition method, finite difference method, B-spline finite element method and boundary element method. The results show that the local discontinuous Galerkin method is one of the most efficient methods for solving the Burgers’ equation. Even with small viscosity coefficient, it can get the satisfied solution.