拟牛顿流的压力投影稳定化低阶有限元方法分析

Analysis of pressure projection stabilized method of low-order finite elements for quasi-newtonian flow problem

作者对一般的拟牛顿流问题,针对线性/线性和线性/常数两种低阶有限元空间,提出了一种新的稳定化方法.该方法可以看成压力投影稳定化方法从Stokes问题到拟牛顿流问题的推广与发展.在速度属于W^(1,r)(Ω),压力属于L^r'(Ω)(1/r+1/r'=1)下,作者给出了误差估计.服从幂律及Carreau分布的拟牛顿流问题可看成本文的特殊情况.

For a generalized quasi-Newtonian flow problem,a new stabilized method focused on the low order velocity-pressure pairs（linear/linear and linear/constant element） is presented. As a development of pressure projection stabilized method,the authors extend it from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed herein yields estimate bounds which measure the error in the approximation of the velocity in the W^l＇r （Ω） norm and that of the pressure in the L^r＇ （Ω）, （1/ r＋l/r^＇ =1）. The power-law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper.