On finite element approximation and stabilization methods for compressible viscous flows

This work is devoted to the numerical solution of the Navier- Stokes equations for compressible viscous fluids. Finite element approximations and stabilization techniques are addressed. Methods to implement discontinuous approximations for the pressure and the density are presented. An upwinding methodology is being investigated which combines the ideas behind the stream line Petrov-Galerkin method and the flux limiter methods aiming to introduce diffusion only where it is necessary.