A mixed finite element method for a compressible Stokes problem with high Reynolds number Original Research Article

A compressible Stokes system is considered, which may be obtained by simply adding a convective derivative of pressure to the continuity equation of the Stokes system. A mixed method for this system is formulated and the Raviart–Thomas finite element of order l is implemented in the discretization of the method. It is shown that the stability results for the resulting continuous and discrete problems are followed by the inf-sup condition as in either the incompressible fluids or the linear elasticity. Error estimates are derived for each variable: velocity, pressure and the gradient of the velocity. The convergence order is degraded by the convective derivative of pressure but can be improved by a suitable approximation of the ambient velocity β. In particular, the Reynolds number is regarded to be essential in deriving our stability results.