TY - JOUR
T1 - A Priori Error Estimates for Obstacle Optimal Control Problem, Where the Obstacle Is the Control Itself
AU - Dendani , Yazid
AU - Ghanem , Radouen
JO - Journal of Computational Mathematics
VL - 4
SP - 717
EP - 740
PY - 2023
DA - 2023/02
SN - 41
DO - http://doi.org/10.4208/jcm.2110-m2021-0131
UR - https://global-sci.org/intro/article_detail/jcm/21412.html
KW - Optimal control, obstacle problem, finite element, a priori error estimate.
AB - <p style="text-align: justify;">In this paper we deal with the convergence analysis of the finite element method for an elliptic penalized unilateral obstacle optimal control problem where the control and the obstacle coincide. Error estimates are established for both state and control variables. We apply a fixed point type iteration method to solve the discretized problem.<br/>To corroborate our error estimations and the efficiency of our algorithms, the convergence results and numerical experiments are illustrated by concrete examples.</p>