|Authors||K. H. Karlsen and T. K. Karper|
|Title||A Convergent Nonconforming Finite Element Method for Compressible Stokes Flow|
|Afilliation||Center for Biomedical Computing (SFF), Scientific Computing|
|Project(s)||Center for Biomedical Computing (SFF)|
|Publication Type||Journal Article|
|Year of Publication||2010|
|Journal||SIAM Journal on Numerical Analysis|
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.