A Dual Mixed Formulation for Non-isothermal Oldroyd-Stokes Problem
Résumé
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.