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Article Dans Une Revue Mathematics of Computation Année : 2009

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

Résumé

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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Dates et versions

hal-00198724 , version 1 (17-12-2007)
hal-00198724 , version 2 (18-09-2008)

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Thierry Gallouët, Raphaele Herbin, Jean-Claude Latché. A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem Part I -- the isothermal case. Mathematics of Computation, 2009, 78 (267), pp.1333-1352. ⟨hal-00198724v2⟩
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