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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.

Numerical analysis of streamline diffusion method for compressible flows