Open Access
august 2010 Mixed finite element-finite volume methods
Naceur Achtaich, Mohamed Chagdali, Khadija Zine Dine
Bull. Belg. Math. Soc. Simon Stevin 17(3): 385-410 (august 2010). DOI: 10.36045/bbms/1284570729


This paper is devoted to present a numerical methods for a model of incompressible and miscible flow in porous media. We analyze a numerical scheme combining a mixed finite element method (MFE) and finite volume scheme (FV) for solving a coupled system includes an elliptic equation (pressure and velocity) and a linear convection-diffusion equation (concentration). The (FV) scheme considered is "vertex centered" type semi implicit. We show that this scheme is $L^{\infty}$, BV stable under a CFL condition and satisfies a discrete maximum principle. We prove also the convergence of the approximate solution obtained by the combined scheme (MFE)-(FV) to the solution of the coupled system. Finally the numerical results are presented for two spaces dimensions problem in a homogenous isotropic medium.


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Naceur Achtaich. Mohamed Chagdali. Khadija Zine Dine. "Mixed finite element-finite volume methods." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 385 - 410, august 2010.


Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 05798740
MathSciNet: MR2731365
Digital Object Identifier: 10.36045/bbms/1284570729

Primary: 35J20 , 65N12 , 76M12 , 76S05

Keywords: convection-diffusion equation , elliptic equation , finite volume scheme , Mixed finite element , porous media

Rights: Copyright © 2010 The Belgian Mathematical Society

Vol.17 • No. 3 • august 2010
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