Baranger, J.; Georget, P.; Najib, K. Error estimates for a mixed finite element method for a non-Newtonian flow. (English) Zbl 0619.76003 J. Non-Newtonian Fluid Mech. 23, 415-421 (1987). We consider in this paper two models of generalized Newtonian fluids, the Carreau viscosity expression and the power law. The calculation of flows following these laws is considered in a mixed formulation and approximated by a conforming triangular finite-element method of Taylor Hood type using \(P_ 2\) continuous approximation of the velocity and \(P_ 1\) continuous approximation of the pressure. The purpose of the paper is to describe the dependence of the numerical efficiency of the method with respect to the chosen law and in particular to the exponent in the power law. For a Carreau model with a strictly positive second plateau this efficiency is the same as for a Newtonian fluid. For a power law with exponent n-1 the efficiency decreases from the Newtonian case, \(n=1\), to the limit case, \(n=0\). Cited in 9 Documents MSC: 76A05 Non-Newtonian fluids 76M99 Basic methods in fluid mechanics 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:generalized Newtonian fluids; Carreau viscosity expression; power law; triangular finite-element method; continuous approximation of the pressure; numerical efficiency; Carreau model × Cite Format Result Cite Review PDF Full Text: DOI