@article{ZHANG2024, 
author = {Xindan ZHANG and Jianping ZHAO and Yanren HOU},
title = {Fully Discrete Finite Element Method Based on the Crank-Nicolson Scheme for Parabolic Optimal Control Problem},
year = {2024},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {41},
number = {2},
pages = {196-205,245},
keywords = {parabolic optimal control problem, Crank-Nicolson scheme, optimality system},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2023.05.18.0001},
doi = {10.13568/j.cnki.651094.651316.2023.05.18.0001},
abstract = {Aiming at parabolic optimal control problem with integral control constraints, a fully discrete finite element method based on Crank-Nicolson scheme is proposed. The state is discretized by piecewise linear finite elements for the space discretization, Crank-Nicolson scheme for time discretization, and the control variables are approximated by piecewise linear function approximation, so as to obtain a discrete optimal system. The error estimates of state variables, adjoint state variables and control variables are proved, and the theoretical results are verified by numerical examples.}
}