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We explore the convergence rate of the Ka\v{c}anov iteration scheme fordifferent models of shear-thinning fluids, including Carreau and power-law typeexplicit quasi-Newtonian constitutive laws. It is shown that the energydifference contracts along the sequence generated by the iteration. Inaddition, an a posteriori computable contraction factor is proposed, whichimproves, on finite-dimensional Galerkin spaces, previously derived bounds onthe contraction factor in the context of the power-law model. Significantly,this factor is shown to be independent of the choice of the cut-off parameterswhose use was proposed in the literature for the Ka\v{c}anov iteration appliedto the power-law model. Our analytical findings are confirmed by a series ofnumerical experiments.

On the convergence rate of the Ka\v{c}anov scheme for shear-thinning fluids