A Posteriori Error Estimation for a Dual Mixed Finite Element Method for Quasi–newtonian Flows Whose Viscosity Obeys a Power Law or Carreau Law

Abstract: A dual mixed finite element method, for quasi–Newtonian fluid flow obeying the power law or the Carreau law, is constructed and analyzed in Farhloul–Zine [13]. This mixed formulation possesses good local (i.e., at element level) conservation properties (conservation of the momentum and the mass) as in the finite volume methods. In Farhloul–Zine [12], we developed an a posteriori error analysis for a non–Newtonian fluid flow problems. The analysis is based on the fact that the equation describing the extra–stress tensor in terms of the rate of strain tensor is invertible and may give the rate of strain tensor as a function of the stress tensor. To free ourselves from this constraint of inversion of laws, and as a generalization of the obtained results in [12], we propose in this work an a posteriori error analysis to this mixed formulation.