[1]黄蓉,姚梦丽,翁智峰.对流扩散方程最优控制问题的重心插值配点格式[J].华侨大学学报(自然科学版),2023,44(3):407-416.[doi:10.11830/ISSN.1000-5013.202203023]
　HUANG Rong,YAO Mengli,WENG Zhifeng.Barycentric Interpolation Collocation Format for Optimal Control Problem of Convection-Diffusion Equation[J].Journal of Huaqiao University(Natural Science),2023,44(3):407-416.[doi:10.11830/ISSN.1000-5013.202203023]
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对流扩散方程最优控制问题的重心插值配点格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第44卷
期数:
2023年第3期
页码:
407-416
栏目:
出版日期:
2023-05-12

文章信息/Info

Title:
Barycentric Interpolation Collocation Format for Optimal Control Problem of Convection-Diffusion Equation
文章编号:
1000-5013(2023)03-0407-10
作者:
黄蓉;  姚梦丽;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
HUANG Rong;  YAO Mengli;  WENG Zhifeng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
重心插值配点格式;  对流扩散方程;  最优控制问题;  误差分析;  Lagrange乘子法
Keywords:
barycentric interpolation collocation format;  convection-diffusion equation;  optimal control problem;  error analysis;  Lagrange multiplier method
分类号:
O241.82
DOI:
10.11830/ISSN.1000-5013.202203023
文献标志码:
A
摘要:
为了讨论对流扩散方程最优控制问题的重心插值配点格式,首先,借助Lagrange乘子法,推导出由状态方程、伴随方程、最优性方程构成的最优性条件.其次,在空间x,y方向均运用重心插值配点格式离散方程组,并给出该配点格式的相容性分析.最后,数值实验验证格式的有效性,与经典有限差分格式比较,重心插值配点格式用较少的节点数就能具有很高的精度.
Abstract:
The barycentric interpolation collocation format for optimal control problem of convection-diffusion equationis considered. Firstly, the optimality conditions which are composed of the state equation, adjoint equation and optimality equation are derived by Lagrange multiplier method. Secondly, the barycentric interpolation collocation format is used to discretize equations in the directions of x and y in space, and the consistent error analysis of the collocation format is also given. Finally, numerical experiments verify the effectiveness of the collocation format. Compared with the classical finite difference format, the barycentric interpolation collocation format has higher accuracy with fewer node numbers.

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备注/Memo

备注/Memo:
收稿日期: 2022-03-02
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); 中央高校基本科研业务费专项资金资助项目(ZQN-702)
更新日期/Last Update: 2023-05-20