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

机译:黏度服从幂定律或Carreau定律的拟牛顿流的双混合有限元方法

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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.
机译:这项工作的目的是针对准牛顿流遵守Carreau或幂定律的双重混合有限元方法的构造。该方法基于引入应力张量作为新变量,以及将控制方程式重新制定为双重鞍点问题。如同有限体积法一样,导出的配方具有局部(即元素级)守恒特性(动量和质量守恒)。基于这样的表述,构造并分析了混合有限元。我们证明了连续问题及其逼近是正确的,并导出了误差估计。

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