2009/06/25 by Kenneth H. Karlsen, Karlsen, Kenneth H., Trygve K. Karper +1
Chemical Engineering · Engineering · #35Q30 #65M12 #74S05 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.0906.4665
openalex publication_date 2009/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.