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.
MSC2010: 35Q30,65N12,65N08,65N30
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References
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.
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Fettah, A., Gallouët, T. (2011). Compressible Stokes Problem with General EOS. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_48
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DOI: https://doi.org/10.1007/978-3-642-20671-9_48
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Online ISBN: 978-3-642-20671-9
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