The streamline-diffusion method for conforming and nonconforming finite elements of lowest order applied to convection-diffusion problems

We consider the streamline-diffusion finite element method with finite elem ents of lowest order for solving convection-diffusion problems. Our investi gations cover both conforming and nonconforming finite element approximatio ns bn triangular and quadrilateral meshes. Although the considered finite e lements are of the same interpolation order their stability and approximati on properties are quite different. We give a detailed overview an the stabi lity and the convergence properties in the L-2- and in the streamline-diffu sion norm. Numerical experiments show that often the theoretical prediction s on the convergence properties are sharp.