Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space

Pedro Merino; Fredi Tröltzsch; Boris Vexler

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 1, page 167-188
  • ISSN: 0764-583X

Abstract

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The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.

How to cite

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Merino, Pedro, Tröltzsch, Fredi, and Vexler, Boris. "Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space." ESAIM: Mathematical Modelling and Numerical Analysis 44.1 (2010): 167-188. <http://eudml.org/doc/250820>.

@article{Merino2010,
abstract = { The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls. },
author = {Merino, Pedro, Tröltzsch, Fredi, Vexler, Boris},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Finite element approximation; optimal control problem; finitely many pointwise state constraints; finite element; optimal control; semilinear elliptic partial differential equation; optimal error estimates},
language = {eng},
month = {3},
number = {1},
pages = {167-188},
publisher = {EDP Sciences},
title = {Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space},
url = {http://eudml.org/doc/250820},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Merino, Pedro
AU - Tröltzsch, Fredi
AU - Vexler, Boris
TI - Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 44
IS - 1
SP - 167
EP - 188
AB - The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
LA - eng
KW - Finite element approximation; optimal control problem; finitely many pointwise state constraints; finite element; optimal control; semilinear elliptic partial differential equation; optimal error estimates
UR - http://eudml.org/doc/250820
ER -

References

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