Convergent finite element methods for compressible barotropic Stokes   systems
  We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete density, equations for the discrete effective viscous flux, and renormalized formulations of the numerical method for the density equation. 
Kenneth H. Karlsen and Trygve K. Karper