Optimal error estimate for a mixed finite element method for compressible Navier–Stokes system Original Research Article

A linearized stationary compressible viscous Navier–Stokes system is considered. A mixed finite element method is applied and the unique existence of the solution is established by the inf–sup condition. The convection terms, especially in the continuity equation, were thought of causing non-optimal order convergence, but in this paper error estimates of optimal order are derived by implementing the lowest order Raviart–Thomas elements. The error estimates for the normal and tangential components of velocity are also optimal on the interfaces of the interior triangles. It turns out that the non-symmetric discrete system can be reformulated into a symmetric form.