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

Mohamed Farhloul (1) , Abdelmalek Zine (2)

1 Département de Mathématiques et de Statistiques-Université de Moncton
2 MMCS - Modélisation mathématique, calcul scientifique

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.

Mots clés: Mixed Finite Element; Quasi–Newtonian; Power law; Carreau law

Domaines: Analyse numérique [math.NA]

Mohamed Farhloul, Abdelmalek Zine. A dual–mixed finite element method for quasi–Newtonian flows whose viscosity obeys a power law or the Carreau law. 2016. ⟨hal-01418324⟩