Convergence of a mixed finite element finite volume scheme for the   isentropic Navier-Stokes system via dissipative measure-valued solutions
  We study convergence of a mixed finite element finite volume numerical scheme for the isentropic Navier-Stokes system under the full range of the adiabatic exponent. We establish suitable stability and consistency estimates and show that the Young measure generated by numerical solutions represents a dissipative measure-valued solutions of the limit system. In particular, using the recently established weak{strong uniqueness principle in the class of dissipative measure-valued solutions we show that the numerical solutions converge strongly to a strong solutions of the limit system as long as the latter exists. 
Eduard Feireisl, Maria Lukacova-Medvidova
math.AP