《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (1): 23-32.

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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

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

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.

• O241.82
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