TY - JOUR
T1 - Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems
AU - Manohar , Ram
AU - Kumar Sinha , Rajen
JO - Journal of Computational Mathematics
VL - 2
SP - 147
EP - 176
PY - 2022
DA - 2022/01
SN - 40
DO - http://doi.org/10.4208/jcm.2009-m2019-0194
UR - https://global-sci.org/intro/article_detail/jcm/20182.html
KW - Semilinear parabolic optimal control problem, Finite element method, The backward Euler method, Elliptic reconstruction, A posteriori error estimates.
AB - <p style="text-align: justify;">This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment&nbsp; is performed to illustrate the performance of the derived estimators.</p>