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计算数学  2013, Vol. 35 Issue (1): 99-112    DOI:
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非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法
孔花1, 冯民富2, 覃燕梅3
1. 内江师范学院, 数学与信息科学学院/四川省高等学校数值仿真重点实验室, 四川内江, 641112;
2. 四川大学数学学院, 成都 610064;
3. 数学与信息科学学院/四川省高等学校数值仿真重点实验室, 四川内江, 641112
A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS
Kong Hua1, Feng Minfu2, Qin Yanmei3
1. Colledge of Mathematics and Information Sciences/Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang Normal University, Neijiang 641112, Sichuan, China;
2. College of Mathematics, Sichuan University, Chengdu 610064, China;
3. Colledge of Mathematics and Information Sciences/Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang Normal University, Neijiang 641112, Sichuan, China
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摘要 本文结合子格粘性法的思想,空间采用非协调Crouzeix-Raviart元逼近,时间采用Crank-Nicolson差分离散,对非定常线性化Navier-Stokes方程建立了全离散的子格粘性非协调有限元格式.对稳定性和误差估计作出了详细的分析, 得出了最优的误差估计.最后, 通过数值算例进一步验证了该方法的稳定性和收敛性.
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关键词非定常线性化Navier-Stokes方程   子格粘性方法   Crouzeix-Raviart元     
Abstract: For the non-stationary linearized Navier-Stokes equations, a non-conforming finite element method of subgrid viscosity method is presented, where Crouzeix-Raviart nonconforming finite element is employed, and the Crank-Nicholson scheme is used for time discretization. Stability and convergence of the method is proved. The error estimation results show that the method achieves optimal accuracy with respect to solution regularity. The numerical results were given, which demonstrate the stability and convergence of the method presented.
Key wordsnon-stationary linearized Navier-Stokes equations   subgrid viscosity method   Crouzeix-Raviart element   
收稿日期: 2012-09-20;
基金资助:

国家自然科学基金项目(编号:11271273),四川省教育厅青年基金项目(编号:11ZB175)资助.

通讯作者: 覃艳梅(1980-), 女, 四川青神人, 副教授.E-mail:qinyanmei0809@163.com.     E-mail: qinyanmei0809@163.com
引用本文:   
. 非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法[J]. 计算数学, 2013, 35(1): 99-112.
. A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS[J]. Mathematica Numerica Sinica, 2013, 35(1): 99-112.
 
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