A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case

Details A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case

2007-12-17

arxiv.org/abs/0712.2798v2

Mathematics

Numerical Analysis

Scientific paper

In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, 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.

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