拟Newton流的一种新的稳定化方法

谢春梅; 冯民富

doi:10.3879/j.issn.1000-0887.2010.09.004

拟Newton流的一种新的稳定化方法

doi: 10.3879/j.issn.1000-0887.2010.09.004

谢春梅¹,
冯民富^1,2

电子科技大学应用数学学院,成都 610054;

基金项目: 四川省科技攻关课题资助项目(05GG006-006-2)

详细信息

作者简介:
谢春梅(1983- ),女,四川人,博士生;冯民富,教授(联系人.E-mail:fmf@wtjs.cn).

中图分类号: O241.82
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2010-07-02
- 刊出日期: 2010-09-15

A New Stabilized Method for Quasi-Newtonian Flow

XIE Chun-mei¹,
FENG Min-fu^1,2

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;
School of Mathematics, Sichuan University, Chengdu 610064, P. R. China

摘要

摘要: 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Newton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．
- 拟Newton流 /
- 稳定化方法 /
- 幂律 /
- Carreau 分布 /
- 基于残差的后验估计
Abstract: 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 W^1,r(Ω)norm and that of the pressure in the L^r'(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.
- quasi-Newtonian /
- stabilized method /
- power law model /
- Carreau modle /
- residual-based posterior bound

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参考文献(20)

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