Continuous and Discontinuous Finite Element Methods for Convection-Diffusion Problems: A Comparison

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