@article{Lu2022, 
author = {Zuliang Lu and Fei Cai and Ruixiang Xu and Chunjuan Hou and Xiankui Wu and Yin Yang},
title = {A posteriori error estimates of hp spectral element method for parabolic optimal control problems},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {5220-5240},
keywords = {parabolic optimal control problems, hp spectral element method, a posteriori error estimates},
url = {https://www.sciopen.com/article/10.3934/math.2022291},
doi = {10.3934/math.2022291},
abstract = {In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem. For improve the accuracy of the algorithm and construct an adaptive finite element approximation. Under the Scott-Zhang type quasi-interpolation operator, a        L    2    (      H    1    )  −      L    2    (      L    2    ) posteriori error estimates of the hp spectral element approximated solutions for both the state variables and the control variable are obtained. Adopting two auxiliary equations and stability results, a        L    2    (      L    2    )  −      L    2    (      L    2    ) posteriori error estimates are derived for the hp spectral element approximation of optimal parabolic control problem.}
}