AuthorsK. H. Karlsen and T. K. Karper
TitleA Convergent Nonconforming Finite Element Method for Compressible Stokes Flow
AfilliationCenter for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2010
JournalSIAM Journal on Numerical Analysis
Volume48
Number5
Pagination1846-1876
Date PublishedOctober
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.

DOI10.1137/09076310X
Citation KeySimula.SC.616