A PENALIZED FINITE-ELEMENT METHOD FOR A COMPRESSIBLE STOKES SYSTEM

The linearized steady-state compressible viscous Navier-Stokes equatio ns with constant coefficients are considered in this paper. A penalty method has been applied to the continuity equation. A finite-element f ormulation is constructed by applying a streamline diffusion method to the penalized continuity equation and applying the usual Galerkin met hod to the momentum equations. The resulting finite-element formulatio n is uniquely solvable without requiring any compatibility condition o n the subspaces for velocity and pressure. An error estimate is obtain ed.