The local discontinuous Galerkin method with generalized alternating flux for solving Burger s equation

In this paper, we propose the local discontinuous Galerkin method based on the generalized alternating numerical flux for solving the one-dimensional nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf-Cole transformation, the original equation is transformed into a linear heat conduction equation with homogeneous Neumann boundary conditions. We will show that this method preserves stability. By virtue of the generalized Gauss-Radau projection, we can obtain the sub-optimal rate of convergence in L²-norm of O(hk+1/2 ) with polynomial of degree k and grid size h. Numerical experiments are given to verify the theoretical results.