Finite element error estimation for parabolic optimal control with measurement data

被引：0
作者：
Yang, Xun [1 ]
Luo, Xianbing [1 ]
机构：
[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China
来源：
RESULTS IN APPLIED MATHEMATICS | 2024年 / 22卷
基金：
中国国家自然科学基金;
关键词：
Finite element; Measure data; Parabolic optimal control; Euler method; EQUATIONS; DISCRETIZATION; APPROXIMATIONS;
D O I：
10.1016/j.rinam.2024.100456
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A prior error estimate is considered for the finite element (FE) approximation of a parabolic optimal control (POC) with spatial measurement data. We use conforming linear finite element to discretize the space for the state, piecewise constant for the control, and Euler method to discretize the time. The convergence order O(h(2-s/2) + k(1/2)) in the L-2(0, T, L-2(Omega))-norm of state variable, co-state, and control variable are obtained. To validate our theory, numerical tests are executed.
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页数：17
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