2007/12/17 by Thierry Gallouët, Gallouët, Thierry, Raphaèle Herbin +3
Engineering · Mathematics · #35Q30 #65N12 #65N30 #76M10 #76M12 #76N15 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.0712.2798
openalex publication_date 2007/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state ρ=p, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual finite element techniques. Since the pressure is piecewise constant, the discrete mass balance takes the form of a finite volume scheme, in which we introduce an upwinding of the density, together with two additional stabilization terms. We prove \em a priori estimates for the discrete solution, which yields its existence by a topological degree argument, and then the convergence of the scheme to a solution of the continuous problem.