A dual-mixed finite element method for quasi-Newtonian flows whose viscosity obeys a power law or the Carreau law

The aim of this work is a construction of a dual mixed finite element method for a quasi-Newtonian flow obeying the Carreau or power law. This method is based on the introduction of the stress tensor as a new variable and the reformulation of the governing equations as a twofold saddle point problem. The derived formulation possesses local (i.e. at element level) conservation properties (conservation of the momentum and the mass) as for finite volume methods. Based on such a formulation, a mixed finite element is constructed and analyzed. We prove that the continuous problem and its approximation are well posed, and derive error estimates.