@article{Hou2022, 
author = {Chunjuan Hou and Zuliang Lu and Xuejiao Chen and Xiankui Wu and Fei Cai},
title = {Superconvergence for optimal control problems governed by semilinear parabolic equations},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {9405-9423},
keywords = {finite element approximation, semilinear parabolic equation, optimal control problem, the elliptic projection, L2-orthogonal projection, superconvergence},
url = {https://www.sciopen.com/article/10.3934/math.2022522},
doi = {10.3934/math.2022522},
abstract = {In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard        L    2    (  Ω  )-orthogonal projection and the elliptic projection. Then we present some necessary intermediate variables and their error estimates. At last, we derive the error estimates between the finite element solutions and        L    2  -orthogonal projection or the elliptic projection of the exact solutions.}
}