| 非定常线性化Navier-Stokes方程的子格粘性非协调有限元方法 |
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| 引用本文： | 孔花,冯民富,覃燕梅.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. |
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| 作者姓名： | 孔花 冯民富 覃燕梅 |
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| 作者单位： | 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 |
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| 基金项目： | 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 |
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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 |
| 收稿时间： | 2012-09-20; |
A NON-CONFORMING FINITE ELEMENT METHOD OF SUBGRID VISCOSITY METHOD FOR THE NON-STATIONARY LINEARIZED NAVIER-STOKES EQUATIONS |
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| Kong Hua
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Feng Minfu
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Qin Yanmei.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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| Authors: | Kong Hua Feng Minfu Qin Yanmei |
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| Institution: | 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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| 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. |
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| Keywords: | non-stationary linearized Navier-Stokes equations subgrid viscosity method Crouzeix-Raviart element |
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