Analysis of a DG method for singularly perturbed convection-diffusion problems

In this article, we studied a discontinuous Galerkin finite element method for convection-diffusion-reaction problems with singular perturbation. Our approach is highly flexible by allowing the use of discontinuous approximating function on polytopal mesh without imposing extra conditions on the convection coefficient. A priori error estimate is devised in a suitable energy norm on general polytopal mesh. Numerical examples are provided.