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Erscheinungsjahr: 
2020
Quellenangabe: 
[Journal:] Computational Optimization and Applications [ISSN:] 1573-2894 [Volume:] 76 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2020 [Pages:] 155-199
Verlag: 
Springer US, New York, NY
Zusammenfassung: 
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.
Schlagwörter: 
Bilinear boundary control
Identification of Robin parameter
Finite element error estimates
Postprocessing approach
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