A priori error estimates of Crank-Nicolson finite element method for parabolic optimal control problems

被引：0
|
作者：
Zhang, Xindan [1 ]
Zhao, Jianping [1 ,2 ]
Hou, Yanren [1 ,3 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
[2] Xinjiang Univ, Inst Math & Phys, Urumqi 830046, Peoples R China
[3] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2023年 / 144卷
基金：
中国国家自然科学基金;
关键词：
Optimal control problem; Parabolic equation; Finite element method; Crank-Nicolson; VARIATIONAL DISCRETIZATION; SUPERCONVERGENCE; APPROXIMATION;
D O I：
10.1016/j.camwa.2023.06.017
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the fully discrete finite element approximation for parabolic optimal control problems with pointwise control constraints is studied. We use standard piecewise linear finite elements for the space discretization of the state, and Crank-Nicolson scheme for time discretization. For control discretization we consider piecewise linear finite elements approximation and variational discretization. We derive a priori error estimates for state, adjoint state and control. Finally, some numerical examples are provided to confirm our theoretical results.
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页码：274 / 289
页数：16
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