拟Newton流的一种新的稳定化方法

A New Stabilized Method for Quasi-Newtonian Flow

对一般的拟Newton流问题,针对(双)线性/(双)线性和(双)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New-ton流问题的推广与发展.在速度属于W1,r(Ω),压力属于Lr'(Ω)(1/r+1/r'=1)下,给出了误差估计.服从幂律及Carreau分布的拟Newton流问题可看成该文的特殊情况.进一步地,还给出了基于残差的后验误差估计.最后给出的数值算例验证了理论结果.

For a generalized quasi-Newtonian flow,a new stabilized method focused on the low order velocity-pressure pairs（（bi） linear/（bi） linear and（bi） linear/constant element） was presented.A development of pressure projection stabilized method was extended from Stokes problems to quasi-Newtonian flow problems.The theoretical framework developed herein yielded an estimate bound which measured the error in the approximation of the velocity in the W1,r（Ω） norm and that of the pressure in the Lr＇（Ω）,（1/r ＋1/r＇ =1）.The power-law model and the Carreau model were special ones of the quasi-Newtonian flow problem discussed.Moreover,a residual-based posterior bound was given.Finally,numerical experiments were presented to confirm our theoretical results.