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

Published online by Cambridge University Press:  16 December 2009

Pedro Merino ,
Fredi Tröltzsch  and
Boris Vexler
Pedro Merino
Affiliation:
Department of Mathematics, EPN Quito, Ecuador.
Fredi Tröltzsch
Affiliation:
Institut für Mathematik, TU Berlin, Germany. troeltz@math.TU-Berlin.DE
Boris Vexler
Affiliation:
Institut für Mathematik, TU Berlin, Germany. troeltz@math.TU-Berlin.DE
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Abstract

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

Keywords

Finite element approximationoptimal control problemfinitely many pointwise state constraints
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 1 , January 2010 , pp. 167 - 188
Copyright
© EDP Sciences, SMAI, 2009

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