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

doi:10.1051/m2an/2009045

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

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Pages (from-to)	167-188
Number of pages	22
Journal	Mathematical Modelling and Numerical Analysis
Volume	44
Issue number	1
DOIs	https://doi.org/10.1051/m2an/2009045
State	Published - 2010
Externally published	Yes

Keywords

Finite element approximation
Finitely many pointwise state constraints
Optimal control problem

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10.1051/m2an/2009045

Cite this

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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.",

keywords = "Finite element approximation, Finitely many pointwise state constraints, Optimal control problem",

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AU - Merino, Pedro

AU - Tröltzsch, Fredi

AU - Vexler, Boris

PY - 2010

Y1 - 2010

N2 - 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.

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.

KW - Finite element approximation

KW - Finitely many pointwise state constraints

KW - Optimal control problem

UR - https://www.scopus.com/pages/publications/77950159686

U2 - 10.1051/m2an/2009045

DO - 10.1051/m2an/2009045

M3 - Article

AN - SCOPUS:77950159686

SN - 2822-7840

VL - 44

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JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 1

ER -

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

Abstract

Keywords

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