Analysis of the SDFEM in a modified streamline diffusion norm for singularly perturbed convection diffusion problems

Abstract: In this paper we consider a model singularly perturbed convection diffusion problem which is solved by a streamline diffusion finite element method (SDFEM) on a Shishkin rectangular mesh. To put insight into the influences of stabilization parameters on SDFEM's solutions, we discuss how to obtain the uniform estimates in the streamline diffusion norm which have not been analyzed up to now. By decreasing the standard stabilization parameters properly near the exponential layers, we obtain the uniform estimates in a norm, which is stronger than the $\varepsilon-$energy norm and weaker than the standard streamline diffusion norm. Numerical experiments show that the presented stabilization parameters provide enough stability for the numerical schemes and yield same accurate solutions as the standard ones.