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Title: Weak-duality based adaptive finite element methods for PDE-constrained optimization with pointwise gradient state-constraints
Authors: Hintermüller, M.Hinze, M.Hoppe, Ronald H. W.
Publishers Version: https://doi.org/10.14760/OWP-2010-15
Issue Date: 2010
Published in: Oberwolfach Preprints (OWP), Volume 2010-15, ISSN 1864-7596
Publisher: Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
Abstract: Adaptive finite element methods for optimization problems for second order linear elliptic partial di erential equations subject to pointwise constraints on the ℓ2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint quali cation such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.
Keywords: Adaptive finite element method; a poststeriori errors; dualization; low regularity; pointwise gradient constrains; state constraints; weak solutions
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik



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