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For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.  相似文献   
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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, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate 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 are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.  相似文献   
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谢春梅  骆艳  冯民富 《计算数学》2011,33(2):133-144
本文对Darcy-Stokes问题提出了一种统一的稳定化有限体积法.在离散问题中,采用两种剖分,一种为三角形剖分,一种为其对偶四边形剖分.速度及压力分别采用非协调线性元及分片常数元来做逼近.经证明,文中的统一格式,具有稳定性及最优误差估计.最后用数值算例验证了本文的理论结果.  相似文献   
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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.  相似文献   
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