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university of Provence - Aix-Marseille I |  |
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university of Provence - Aix-Marseille I | |
| HAL: hal-00359140, version 1 |
| DOI: 10.1090/S0025-5718-09-02310-2 |
| Detailed view |  Export this paper |
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| Math. Comp. 79, 270 (2010) 649--675 |
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| A convergent Finite Element-Finite Volume scheme for the compressible Stokes problem, Part II -- the isentropic case |
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| Robert Eymard 1Thierry Gallouët 2 |
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| (2010) |
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| In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with an equation of state of the form $p=\rho^\gamma$ (where $p$ stands for the pressure and $\rho$ for the density). 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 stabilization terms. We prove {\em a priori} estimates for the discrete solution, which yield its existence. Then the convergence of the scheme to a solution of the continuous problem is established. The passage to the limit in the equation of state requires the a.e. convergence of the density. It is obtained by adapting at the discrete level the "effective viscous pressure lemma" of the theory of compressible Navier-Stokes equations. |
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| 1: | Laboratoire d'Etudes des Transferts d'Energie et de Matière (LETEM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) : EA2546 |
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| 2: | Laboratoire d'Analyse, Topologie, Probabilités (LATP) |
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CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III |
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| 3: | Institut de radioprotection et de sûreté nucléaire (IRSN) |
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Ministère de l'écologie de l'Energie, du Développement durable et de l'Aménagement du territoire – Ministère de l'économie, de l'industrie et de l'emploi – Ministère de l'Enseignement Supérieur et de la Recherche Scientifique – Ministère de la Défense – Ministère de la santé |
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| Subject | : | Mathematics/Numerical Analysis |
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| Compressible Stokes equations – finite element methods – finite volume methods |
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| hal-00359140, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00359140 | |
| oai:hal.archives-ouvertes.fr:hal-00359140 | |
| From: Raphaele Herbin | |
| Submitted on: Thursday, 5 February 2009 18:39:10 | |
| Updated on: Friday, 29 October 2010 22:00:37 | |
