In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Kármán equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed to discretize the state and adjoint variables. The control is discretized using piece-wise constant approximations. A priori error estimates are derived for the state, adjoint and control variables. Numerical results that justify the theoretical results are presented.
Accepté le :
DOI : 10.1051/m2an/2018023
Keywords: von Kármán equations, distributed control, plate bending, semilinear, conforming finite element methods, error estimates.
Mallik, Gouranga 1 ; Nataraj, Neela 1 ; Raymond, Jean-Pierre 1
@article{M2AN_2018__52_3_1137_0,
author = {Mallik, Gouranga and Nataraj, Neela and Raymond, Jean-Pierre},
title = {Error estimates for the numerical approximation of a distributed optimal control problem governed by the von {K\'arm\'an} equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1137--1172},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {3},
doi = {10.1051/m2an/2018023},
zbl = {1405.65153},
mrnumber = {3865561},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2018023/}
}
TY - JOUR AU - Mallik, Gouranga AU - Nataraj, Neela AU - Raymond, Jean-Pierre TI - Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1137 EP - 1172 VL - 52 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2018023/ DO - 10.1051/m2an/2018023 LA - en ID - M2AN_2018__52_3_1137_0 ER -
%0 Journal Article %A Mallik, Gouranga %A Nataraj, Neela %A Raymond, Jean-Pierre %T Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1137-1172 %V 52 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2018023/ %R 10.1051/m2an/2018023 %G en %F M2AN_2018__52_3_1137_0
Mallik, Gouranga; Nataraj, Neela; Raymond, Jean-Pierre. Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Kármán equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 3, pp. 1137-1172. doi: 10.1051/m2an/2018023
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