The local discontinuous Galerkin finite element method for a class of convection-diffusion equations

In this paper, we study the local discontinuous Galerkin (LOG) finite element method for solving a class of convection-diffusion equations with the first-kind boundary conditions. Based on the Hopf-Cole transformation, we transform the original equation into a linear heat equation with the same kind boundary conditions. Then the heat equation is solved by the LOG finite element method with a suitably chosen numerical flux. Theoretical analysis shows that this method is stable and has a (k + 1)-th order of convergence rate when the polynomials P-k are used. Finally, numerical experiments for one-dimensional and two-dimensional convection-diffusion equations are given to confirm the theoretical results. (C) 2012 Elsevier Ltd. All rights reserved.