The goal of this paper is to derive some error estimates for the numerical discretization of some optimal control problems governed by semilinear elliptic equations with bound constraints on the control and a finitely number of equality and inequality state constraints. We prove some error estimates for the optimal controls in the norm and we also obtain error estimates for the Lagrange multipliers associated to the state constraints as well as for the optimal states and optimal adjoint states.
Mots clés : distributed control, state constraints, semilinear elliptic equation, numerical approximation, finite element method, error estimates
@article{COCV_2002__8__345_0,
author = {Casas, Eduardo},
title = {Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {345--374},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002049},
mrnumber = {1932955},
zbl = {1066.49018},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv:2002049/}
}
TY - JOUR AU - Casas, Eduardo TI - Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2002 SP - 345 EP - 374 VL - 8 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2002049/ DO - 10.1051/cocv:2002049 LA - en ID - COCV_2002__8__345_0 ER -
%0 Journal Article %A Casas, Eduardo %T Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 345-374 %V 8 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2002049/ %R 10.1051/cocv:2002049 %G en %F COCV_2002__8__345_0
Casas, Eduardo. Error estimates for the numerical approximation of semilinear elliptic control problems with finitely many state constraints. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 345-374. doi : 10.1051/cocv:2002049. http://archive.numdam.org/articles/10.1051/cocv:2002049/
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