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

Mohamed Farhloul and Abdelmalek Zine

Mathematics and Computers in Simulation (MATCOM), 2017, vol. 141, issue C, 83-95

Abstract: 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.

Keywords: Mixed finite element; Quasi-Newtonian; Power law; Carreau law (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:141:y:2017:i:c:p:83-95

DOI: 10.1016/j.matcom.2016.09.015

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