Authors | K. H. Karlsen and T. K. Karper |
Title | A Convergent Nonconforming Finite Element Method for Compressible Stokes Flow |
Afilliation | , Scientific Computing |
Project(s) | Center for Biomedical Computing (SFF) |
Status | Published |
Publication Type | Journal Article |
Year of Publication | 2010 |
Journal | SIAM Journal on Numerical Analysis |
Volume | 48 |
Number | 5 |
Pagination | 1846-1876 |
Date Published | October |
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. |
DOI | 10.1137/09076310X |
Citation Key | Simula.SC.616 |