Mathematics – Numerical Analysis
Scientific paper
2009-04-04
Mathematics
Numerical Analysis
Scientific paper
We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nedelec spaces of the first kind. The continuity equation is approximated by a standard piecewise constant upwind discontinuous Galerkin scheme. Our main result states that the numerical method converges to a weak solution. The convergence proof consists of two main steps: (i) To establish strong spatial compactness of the velocity field, which is intricate since the element spaces are only div or curl conforming. (ii) To prove that the discontinuous Galerkin approximations converge strongly, which is required in view of the nonlinear pressure function. Tools involved in the analysis include a higher integrability estimate for the discontinuous Galerkin approximations, a discrete equation for the effective viscous flux, and various renormalized formulations of the discontinuous Galerkin scheme.
Karlsen Kenneth H.
Karper Trygve K.
No associations
LandOfFree
Convergence of a mixed method for a semi-stationary compressible Stokes system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Convergence of a mixed method for a semi-stationary compressible Stokes system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence of a mixed method for a semi-stationary compressible Stokes system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-123302