@article{11236,
  author = {Kenneth Karlsen and Trygve Karper},
  title = {A Convergent Nonconforming Finite Element Method for Compressible Stokes Flow},
  abstract = {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.},
  year = {2010},
  journal = {SIAM Journal on Numerical Analysis},
  volume = {48},
  number = {5},
  pages = {1846-1876},
  month = {October},
  doi = {10.1137/09076310X},
}