We study a finite element method for the linearized stationary compressible viscous Stokes system in a bounded domain with extra streamline diffusion added to the continuity equation. The differential equations to be considered are ?? Here, $\U$ is a given ambient fluid velocity vector and $\r=\r(P)$ is the density function of a given ambient fluid pressure $p$, and depending on the vector field $\U$, two different problems are considered. The unique existence and convergence analysis of the corresponding approximate solution is shown and numerical examples are given.
