Numerical performance of discontinuous and stabilized continuous Galerkin methods for convection–diffusion problems

We compare the performance of two classes of numerical methods for the approximation of linear steady–state convection–diffusion equations, namely, the discontinuous Galerkin (DG) method and the continuous stream- line upwind Petrov-Galerkin (SUPG) method. We present a fair comparison of such schemes considering both diffusion–dominated and convection–dominated regimes, and present numerical results obtained on a series of test problems including smooth solutions, and test cases with sharp internal and boundary layers.