[1]赖艺颖,滕宇航,翁智峰.椭圆最优控制问题的稳定化混合有限元方法[J].华侨大学学报(自然科学版),2025,46(6):722-728.[doi:10.11830/ISSN.1000-5013.202408007]
　LAI Yiying,TENG Yuhang,WENG Zhifeng.Stabilization Mixed Finite Element Method of Elliptic Optimal Control Problem[J].Journal of Huaqiao University(Natural Science),2025,46(6):722-728.[doi:10.11830/ISSN.1000-5013.202408007]
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椭圆最优控制问题的稳定化混合有限元方法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第46卷
期数:
2025年第6期
页码:
722-728
栏目:
出版日期:
2025-11-20

文章信息/Info

Title:
Stabilization Mixed Finite Element Method of Elliptic Optimal Control Problem
文章编号:
1000-5013(2025)06-0722-07
作者:
赖艺颖;  滕宇航;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LAI Yiying;  TENG Yuhang;  WENG Zhifeng
School of Mathematical Science, Huaqiao University, Quanzhou 362021, China
关键词:
无约束椭圆最优控制问题;  稳定化混合有限元;  低次等阶有限元对;  误差估计
Keywords:
unconstrained elliptic optimal control problem;  stabilization mixed finite element;  low order equal rank finite element pair;  error estimation
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202408007
文献标志码:
A
摘要:
采用低次等阶混合元结合局部高斯积分稳定化方法求解无约束椭圆最优控制问题。首先,结合变分原理和最优化理论,将求解椭圆最优控制问题转化为状态方程、对偶方程和最优性条件三者的联立系统。其次,构造椭圆最优控制问题的稳定化混合元格式,并分析该格式的误差估计。最后,通过数值算例验证格式的有效性。
Abstract:
Low order equal rank mixed elements combined with local Gauss integration stabilization method to solve unconstrained elliptical optimal control problems are used. Firstly, combining the variational principle and optimization theory, the solution to the elliptic optimal control problem is transformed into an associative system of state equation, dual equation and optimality condition. Secondly, the stabilization mixed element schemes of the elliptical optimal control problem are constructed, and the error estimations of these schemes are analyzed. Finally, the effectiveness of the schemes are verified through numerical examples.

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备注/Memo

备注/Memo:
收稿日期: 2024-08-07
通信作者: 翁智峰(1985-),男,副教授,博士,主要从事偏微分方程数值解的研究。E-mail:zfwmath@163.com。
基金项目: 国家自然科学基金资助项目(11701197); 福建省自然科学基金资助项目(2022J01308)
更新日期/Last Update: 2025-11-20