A priori error estimates of finite volume element method for bilinear parabolic optimal control problem

被引：0
|
作者：
Lu, Zuliang [1 ,2 ]
Xu, Ruixiang [3 ]
Hou, Chunjuan [4 ]
Xing, Lu [3 ]
机构：
[1] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Key Lab Intelligent Informat Proc & Control, Chongqing 404000, Peoples R China
[2] Tianjin Univ Finance & Econ, Res Ctr Math & Econ, Tianjin 300222, Peoples R China
[3] Chongqing Three Gorges Univ, Key Lab Nonlinear Sci & Syst Struct, Chongqing 404000, Peoples R China
[4] Guangzhou Huashang Coll, Dept Data Sci, Guangzhou 511300, Peoples R China
来源：
AIMS MATHEMATICS | 2023年 / 8卷 / 08期
基金：
美国国家科学基金会;
关键词：
bilinear parabolic optimal control problems; finite volume element method; APPROXIMATION;
D O I：
10.3934/math.2023988
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the finite volume element method of bilinear parabolic optimal control problem. We will use the optimize-then-discretize approach to obtain the semi-discrete finite volume element scheme for the optimal control problem. Under some reasonable assumptions, we derive the optimal order error estimates in L2(J; L2) and L & DEG;& DEG;(J; L2)-norm. We use the backward Euler method for the discretization of time to get fully discrete finite volume element scheme for the optimal control problem, and obtain some error estimates. The approximate order for the state, costate and control variables is O(h3/2 + ot) in the sense of L2(J; L2) and L & DEG;& DEG;(J; L2)-norm. Finally, a numerical experiment is presented to test these theoretical results.
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页码：19374 / 19390
页数：17
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