Error estimates for the finite element approximation of bilinear boundary control problems

Artikel

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin coefficient from a given measurement of the state, or when the Robin coefficient can be controlled in order to reach a desired state. Necessary and sufficient optimality conditions are derived and several discretization approaches for the numerical solution of the optimal control problem are investigated. Considered are both a full discretization and the postprocessing approach meaning that we compute an improved control by a pointwise evaluation of the first-order optimality condition. For both approaches finite element error estimates are shown and the validity of these results is confirmed by numerical experiments.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Journal: Computational Optimization and Applications ; ISSN: 1573-2894 ; Volume: 76 ; Year: 2020 ; Issue: 1 ; Pages: 155-199 ; New York, NY: Springer US

Klassifikation und Themen

• Klassifikation: Mathematik
• Thema: Bilinear boundary control ; Identification of Robin parameter ; Finite element error estimates ; Postprocessing approach

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Winkler, Max
• Ereignis: Veröffentlichung
• (wer): Springer US
• (wo): New York, NY
• (wann): 2020

Weitere Informationen

• DOI: doi:10.1007/s10589-020-00171-5
• Letzte Aktualisierung: 10.03.2025, 11:44 MEZ