Bibliographic Metadata

Title
Goal-oriented adaptivity in pointwise state constrained optimal control of partial differential equations
AuthorHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Hoppe, Ronald H.W.
Published in
SIAM Journal on Control and Optimization, Philadelphia, Pa., 2010, Vol. 48, Issue 8, page 5468-5487
PublishedSIAM
LanguageEnglish
Document typeJournal Article
Keywords (EN)adaptive finite element method / a posteriori error estimate / pointwise state constraints / goal-oriented adaptivity / PDE-constrained optimization
ISSN1095-7138
URNurn:nbn:at:at-ubg:3-983 Persistent Identifier (URN)
DOIdoi:10.1137/090761823 
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 The work is publicly available
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Abstract (English)

We derive primal-dual weighted goal-oriented a posteriori error estimates for pointwise state constrained optimal control problems for second order elliptic partial differential equations. The constraints give rise to a primal-dual weighted error term representing the mismatch in the complementarity system due to discretization. In the case of sufficiently regular active (or coincidence) sets and problem data, a further decomposition of the multiplier into a regular L2-part on the active set and a singular part concentrated on the boundary between the active and inactive set allows us to further characterize the mismatch error. The paper ends with a report on the behavior of the error estimates for test cases including the case of singular active sets consisting of only smooth curves or points.

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