  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.
