Nonconforming streamline-diffusion-finite-element-methods for convection-diffusion problems

We analyze nonconforming finite element approximations of streamline-diffusion type for solving convection-diffusion problems. Both the theoretical and numerical investigations show that additional jump terms have to be added in the nonconforming case in order to get the same $O(h^{k+1/2})$ order of convergence in L $^2$ as in the conforming case for convection dominated problems. A rigorous error analysis supported by numerical experiments is given.