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Navier-Stokes方程最优控制问题的一种非协调有限元局部稳定化方法

 引用本文: 覃燕梅, 李辉, 冯民富. Navier-Stokes方程最优控制问题的一种非协调有限元局部稳定化方法[J]. 应用数学和力学, 2016, 37(8): 842-855.
QIN Yan-mei, LI Hui, FENG Min-fu. A Local Stabilized Nonconforming Finite Element Method for the Optimal Control of Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(8): 842-855. doi: 10.21656/1000-0887.370137
 Citation: QIN Yan-mei, LI Hui, FENG Min-fu. A Local Stabilized Nonconforming Finite Element Method for the Optimal Control of Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(8): 842-855.

## Navier-Stokes方程最优控制问题的一种非协调有限元局部稳定化方法

##### doi: 10.21656/1000-0887.370137

###### 作者简介:覃燕梅(1980—)，女，副教授，硕士(E-mail: qinyanmei0809@163.com)；冯民富(1964—)，男，教授，博士生导师(通讯作者. E-mail: fmf@wtjs.cn).
• 中图分类号: O241.82

## A Local Stabilized Nonconforming Finite Element Method for the Optimal Control of Navier-Stokes Equations

Funds: The National Natural Science Foundation of China(11271273)
• 摘要: 基于局部Gauss积分和梯形外推公式，速度/压力空间采用最低等阶非协调元NCP1-P1逼近，针对非定常Navier-Stokes方程最优控制问题，建立了一种全离散的非协调有限元局部稳定化格式.该格式绕开了inf-sup条件的束缚，且在每一时间步上，只需要做线性计算，减少了计算量.证明了该格式是无条件稳定的，给出了详细的误差分析.误差结果表明，该线性格式在时间上具有二阶精度.
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##### 出版历程
• 收稿日期:  2016-05-05
• 修回日期:  2016-06-20
• 刊出日期:  2016-08-15

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