# 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

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topMerino, 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 -

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