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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (1): 23-32.doi: 10.6040/j.issn.1671-9352.0.2019.069

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一类捕食与被捕食模型最优控制问题的有限元方法的先验误差估计

郑瑞瑞1,孙同军2*   

  1. 1.山东交通学院理学院, 山东 济南 250357;2.山东大学数学学院, 山东 济南 250100
  • 发布日期:2020-01-10
  • 作者简介:郑瑞瑞(1984— ),女,硕士,讲师,研究方向为偏微分方程最优控制问题的数值解法. E-mail:mathzheng@126.com*通信作者简介:孙同军(1970— ),男,博士,教授,研究方向为偏微分方程最优控制问题的数值解法. E-mail:tjsun@sdu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11871312);山东省自然科学基金资助项目(ZR2018MA007)

A priori error estimates of finite element methods for an optimal control problem governed by a one-prey and one-predator model

ZHENG Rui-rui1, SUN Tong-jun2*   

  1. 1. School of Science, Shandong Jiaotong University, Jinan 250357, Shandong, China;
    2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2020-01-10

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摘要： 讨论了一类具有一个捕食者和一个被捕食者的捕食模型的最优控制问题。利用最优控制理论,推导出对偶状态方程和最优性条件。采用分片线性连续函数对状态变量、对偶状态变量进行逼近,分片常数函数对控制变量进行逼近,建立了模型问题的有限元全离散格式。通过分析,推导得到状态变量、对偶状态变量和控制变量的先验误差估计。

关键词: 捕食与被捕食模型, 最优控制问题, 对偶状态变量, 最优性条件, 先验误差估计

Abstract: An optimal control problem governed by a one-prey and one-predator model is considered. The co-state equations and optimality conditions are established using optimal control theory. In order to construct the fully discrete approximation, the state and co-state variables are approximated by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. A priori error estimates for the state variables, co-state variables and control variable are proved.

Key words: predator and prey model, optimal control problem, co-state variable, optimality condition, priori error estimate

中图分类号: 

  • O241.82
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