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A general theorem on error estimates with application to a quasilinear elliptic optimal control problem

Please always quote using this URN:urn:nbn:de:0296-matheon-9616
  • A theorem on error estimates for smooth nonlinear programming problems in Banach spaces is proved that can be used to derive optimal error estimates for optimal control problems. This theorem is applied to a class of optimal control problems for quasilinear elliptic equations. The state equation is approximated by a finite element scheme, while different discretization methods are used for the control functions. The distance of locally optimal controls to their discrete approximations is estimated.

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Metadaten
Author:Eduardo Casas, Fredi Tröltzsch
URN:urn:nbn:de:0296-matheon-9616
Referee:Michael Hintermüller
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/01/09
Release Date:2012/01/09
Tag:
Institute:Technische Universität Berlin
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J62 Quasilinear elliptic equations
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Preprint Number:848
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