| Issue |
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
|
|
|---|---|---|
| Page(s) | 1655 - 1686 | |
| DOI | https://doi.org/10.1051/m2an/2022040 | |
| Published online | 20 July 2022 | |
A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations
1
Department of Mathematics, The LNM Institute of Information Technology, Jaipur 302031, India
2
School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram 695551, India
3
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
4
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
* Corresponding author: neela@math.iitb.ac.in; nataraj.neela@gmail.com
Received:
16
October
2021
Accepted:
20
April
2022
This article discusses the numerical analysis of the distributed optimal control problem governed by the von Kármán equations defined on a polygonal domain in ℝ2. The state and adjoint variables are discretised using the nonconforming Morley finite element method and the control is discretized using piecewise constant functions. A priori and a posteriori error estimates are derived for the state, adjoint and control variables. The a posteriori error estimates are shown to be efficient. Numerical results that confirm the theoretical estimates are presented.
Mathematics Subject Classification: 65N30 / 65N15 / 49M05 / 49M25
Key words: von Kármán equations / distributed control / plate bending / non-linear / nonconforming / Morley FEM / a priori / a posteriori / error estimates
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.