JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (1): 23-32.doi: 10.6040/j.issn.1671-9352.0.2019.069

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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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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

CLC Number: 

  • O241.82
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