  We propose a nonconforming finite element method for isentropic viscous gas
flow in situations where convective effects may be neglected. We approximate
the continuity equation by a piecewise constant discontinuous Galerkin method.
The velocity (momentum) equation is approximated by a finite element method on
div-curl form using the nonconforming Crouzeix-Raviart space. Our main result
is that the finite element method converges to a weak solution. The main
challenge is to demonstrate the strong convergence of the density
approximations, which is mandatory in view of the nonlinear pressure function.
The analysis makes use of a higher integrability estimate on the density
approximations, an equation for the "effective viscous flux", and renormalized
versions of the discontinuous Galerkin method.

Numerical Analysis;Analysis of PDEs