The local discontinuous Galerkin finite element method for Burger’s equation

Abstract

In this paper, we study the local discontinuous Galerkin (LDG) finite element method for solving a nonlinear Burger’s equation with Dirichlet boundary conditions. Based on the Hopf–Cole transformation, we transform the original problem into a linear heat equation with Neumann boundary conditions. The heat equation is then solved by the LDG finite element method with special chosen numerical flux. Theoretical analysis shows that this method is stable and the ( k + 1 ) th order of convergence rate when the polynomials P k are used. Finally, we present some examples of P k polynomials with 1 ≤ k ≤ 4 to demonstrate the high-order accuracy of this method. The numerical results are also shown to be more accurate than some available results given in the literature.