Numerical approximation of the general compressible Stokes problem

In this paper, we propose a discretization for the compressible Stokes problem with an equation of state of the form p=φ(ρ) (where p stands for the pressure and ρ for the density, and φ is a superlinear nondecreasing function from ℝ to ℝ). This scheme is based on Crouzeix–Raviart approximation spaces. The discretization of the momentum balance is obtained by the usual finite element technique. The discrete mass balance is obtained by a finite volume scheme, with an upwinding of the density, and two additional terms. We prove the existence of a discrete solution and the convergence of this approximate solution to a solution of the continuous problem.