剪切变稀流体Kačanov格式的收敛速度
On the convergence rate of the Kačanov scheme for shear-thinning fluids
摘要：
我们探讨的收敛速度的Kačanov迭代计划的不同模型的剪切变稀流体，包括Carreau和幂律型显式准牛顿本构关系。结果表明，能量差沿迭代产生的序列收缩。此外，一个后验可计算的收缩因子，提出了改进，有限维Galerkin空间，以前推导的范围内的幂律模型的收缩因子。值得注意的是，这个因素被证明是独立的选择的截止参数，其使用提出了在文献中的Kačanov迭代适用于幂律模型。我们的分析结果证实了一系列的数值实验。
英文摘要：
We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constitutive laws. It is shown that the energy difference contracts along the sequence generated by the iteration. In addition, an a posteriori computable contraction factor is proposed, which improves, on finite-dimensional Galerkin spaces, previously derived bounds on the 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 parameters whose use was proposed in the literature for the Kačanov iteration applied to the power-law model. Our analytical findings are confirmed by a series of numerical experiments.
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