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


Authors: T. Gallouët, R. Herbin and J.-C. Latché
Journal: Math. Comp. 78 (2009), 1333-1352
MSC (2000): Primary 35Q30, 65N12, 65N30, 76N15, 76M10, 76M12
DOI: https://doi.org/10.1090/S0025-5718-09-02216-9
Published electronically: January 30, 2009
MathSciNet review: 2501053
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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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Additional Information

T. Gallouët
Affiliation: Université de Provence, France
Email: gallouet@cmi.univ-mrs.fr

R. Herbin
Affiliation: Université de Provence, France
Email: herbin@cmi.univ-mrs.fr

J.-C. Latché
Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN)
Email: jean-claude.latche@irsn.fr

DOI: https://doi.org/10.1090/S0025-5718-09-02216-9
Keywords: Compressible Stokes equations, finite element methods, finite volume methods
Received by editor(s): December 7, 2007
Published electronically: January 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society