A posteriori error analysis for optimization with PDE constraints

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dc.contributor.authorGaspoz, Fernando
dc.contributor.authorKreuzer, Christian
dc.contributor.authorVeeser, Andreas
dc.contributor.authorWollner, Winnifried
dc.date.accessioned2025-03-19T15:10:53Z
dc.date.available2025-03-19T15:10:53Z
dc.date.issued2025-03
dc.description.abstractWe consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.en
dc.identifier.issn2190-1767
dc.identifier.urihttp://hdl.handle.net/2003/43555
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-25388
dc.language.isoen
dc.relation.ispartofseriesErgebnisberichte des Instituts für Angewandte Mathematik; 681de
dc.subject.ddc610
dc.titleA posteriori error analysis for optimization with PDE constraintsen
dc.typeText
dc.type.publicationtypePreprint
dcterms.accessRightsopen access
eldorado.secondarypublicationfalse

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