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Volume 41, Issue 4
A Priori Error Estimates for Obstacle Optimal Control Problem, Where the Obstacle Is the Control Itself

Yazid Dendani & Radouen Ghanem

DOI: 10.4208/jcm.2110-m2021-0131

J. Comp. Math., 41 (2023), pp. 717-740.

Published online: 2023-02

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  • Abstract

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.
To corroborate our error estimations and the efficiency of our algorithms, the convergence results and numerical experiments are illustrated by concrete examples.

  • Keywords

Optimal control, obstacle problem, finite element, a priori error estimate.

  • AMS Subject Headings

49J20, 65M60, 35R35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yazid.dendani@univ-annaba.dz (Yazid Dendani)

redouen.ghanem@univ-annaba.dz (Radouen Ghanem)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-717, author = {Dendani , Yazid and Ghanem , Radouen}, title = {A Priori Error Estimates for Obstacle Optimal Control Problem, Where the Obstacle Is the Control Itself}, journal = {Journal of Computational Mathematics}, year = {2023}, volume = {41}, number = {4}, pages = {717--740}, abstract = {

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.
To corroborate our error estimations and the efficiency of our algorithms, the convergence results and numerical experiments are illustrated by concrete examples.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2110-m2021-0131}, url = {http://global-sci.org/intro/article_detail/jcm/21412.html} }
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 -

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.
To corroborate our error estimations and the efficiency of our algorithms, the convergence results and numerical experiments are illustrated by concrete examples.

Dendani , Yazid and Ghanem , Radouen. (2023). A Priori Error Estimates for Obstacle Optimal Control Problem, Where the Obstacle Is the Control Itself. Journal of Computational Mathematics. 41 (4). 717-740. doi:10.4208/jcm.2110-m2021-0131
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