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Compressible Stokes Problem with General EOS

  • A. FettahEmail author
  • T. Gallouët
Conference paper
Part of the Springer Proceedings in Mathematics book series (PROM, volume 4)

Abstract

In this paper, we propose a discretization for the compressible Stokes problem with an equation of state of the form p = φ(ρ) (where p stands for the pressure, ρ for the density and φ is a nondecreasing function belonging to \({C}^{1}({\mathbb{R}}_{+}, \mathbb{R})\)). This scheme is based on Crouzeix-Raviart approximation spaces. The discretization of the momentum balance is obtained by the usual finite element technique. The discrete mass balance is obtained by a finite volume scheme, with an upwinding of the density, and two additional terms. We prove existence of a discrete solution and convergence of this approximate solution to a solution of the continuous problem.

Keywords

Compressible Stokes finite element finite volume 

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References

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    M. Crouzeix and P.-A. Raviart. Conforming and nonconforming finite element methods for solving the stationary Stokes equations I. Revue Française d’Automatique, Informatique et Recherche Opérationnelle (R.A.I.R.O.), R-3:33–75, 1973.Google Scholar
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    A. Ern and J.-L. Guermond. Theory and practice of finite elements. Number 159 in Applied Mathematical Sciences. Springer, New York, 2004.Google Scholar
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    R. Eymard, T. Gallouët, R. Herbin, and J.-C. Latché. A convergent finite element-finite volume scheme for the compressible Stokes problem. Part II: the isentropic case. to appear in Mathematics of Computation, 2009.Google Scholar
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    T. Gallouët, R. Herbin, and J.-C. Latché. A convergent finite element-finite volume scheme for the compressible Stokes problem. Part I: the isothermal case. Mathematics of Computation, 267:1333–1352, 2009.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Université Aix-MarseilleAix-MarseilleFrance

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