Volume 56, Number 5, September-October 2022
|Page(s)||1655 - 1686|
|Published online||20 July 2022|
A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations
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
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.
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