@article{Li2024, 
author = {Huanhuan Li and Meiling Ding and Xianbing Luo and Shuwen Xiang},
title = {Convergence analysis of finite element approximations for a nonlinear second order hyperbolic optimal control problems},
year = {2024},
journal = {Networks and Heterogeneous Media},
volume = {19},
number = {2},
pages = {842-866},
keywords = {second order hyperbolic equation, optimal control, finite element method, a priori error estimates},
url = {https://www.sciopen.com/article/10.3934/nhm.2024038},
doi = {10.3934/nhm.2024038},
abstract = {This paper focused on approximating a second-order nonlinear hyperbolic optimal control problem. By introducing a new variable, the hyperbolic equation was converted into two parabolic equations. A second-order fully discrete scheme was obtained by combining the Crank-Nicolson formula with the finite element method. The error estimation for this scheme was derived utilizing the second-order sufficient optimality condition and auxiliary problems. To validate the effectiveness of the fully discrete scheme, a numerical example was presented.}
}