Continuous and discontinuous finite element methods for convection-diffusion problems

We compare numerically the performance of a new continuous-discontinuous ?nite element method (CDFEM) for linear convection-di?usion equations with three well-known upwind ?nite element formulations, namely with the streamline upwind Petrov-Galerkin ?nite element method, the residualfree bubble method and the discontinuous Galerkin ?nite element method. The de?ning feature of the CDFEM is that it uses discontinuous approximation spaces in the vicinity of layers while continuous FEM approximation are employed elsewhere.