Geodesic
A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem
M. Farhloul1 ; A. Zine2
1 Département de Mathématiques et de Statistique, Université de Moncton Moncton, N.B., E1A 3E9, Canada
2 Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Institut Camille Jordan 36, rue Guy de Collongue, 69134 Ecully, France
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 130-156.

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We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the both extra stress and the heat flux’s vector are considered. Based on such a formulation, a dual mixed finite element is constructed and analyzed. This finite element method enables us to obtain precise approximations of the dual variable which are, for the non-isothermal fluid flow problems, the viscous and polymeric components of the extra-stress tensor, as well as the heat flux. Furthermore, it has properties analogous to the finite volume methods, namely, the local conservation of the momentum and the mass.
DOI : 10.1051/mmnp/20116507

M. Farhloul 1 ; A. Zine 2

1 Département de Mathématiques et de Statistique, Université de Moncton Moncton, N.B., E1A 3E9, Canada
2 Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Institut Camille Jordan 36, rue Guy de Collongue, 69134 Ecully, France 
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M. Farhloul; A. Zine. A Dual Mixed Formulation for Non-isothermal Oldroyd–Stokes Problem. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 130-156. doi : 10.1051/mmnp/20116507. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116507/

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