Optimal error estimate for a mixed finite element method for compressible Navier--Stokes system

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.

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