The analysis of a finite element method with streamline diffusion for the compressible Navier-Stokes equations

This paper deals with the rigorous error analysis of finite element solutio ns of the two- and three-dimensional nonstationary compressible Navier Stok es equations. The streamline diffusion technique is applied to the continui ty equation to obtain a stabilized finite element scheme. It is proved that the numerical formulation has a unique solution and the solution is conver gent. An a priori error estimate uniform in time is obtained.