Abstract
A linearized steady-state compressible viscous Navier--Stokes system with an inflow boundary condition is considered. A discontinuous Galerkin method for this system is formulated with convection-dominance and O(h) viscous functions where h is the mesh size in a given triangulation. The resulting finite element method is explicit and valid for all polynomials of degree $\geq 1.$ We show a Lp-stability and derive error estimates for velocity and pressure, respectively. In particular, the compressibility number $\k:=\r'/\r$ is regarded as essential in showing our stability results.
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