A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case

Gallouët, T.; Herbin, R.; Latché, J.-C.

doi:10.1090/S0025-5718-09-02216-9

A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: The isothermal case
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by T. Gallouët, R. Herbin and J.-C. Latché PDF

Math. Comp. 78 (2009), 1333-1352 Request permission

Abstract:

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 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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