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Error estimates for a mixed finite element method for a non-Newtonian flow. (English) Zbl 0619.76003

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, \(n=0\).

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
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