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

Max Winkler ()
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Max Winkler: Technische Universität Chemnitz

Computational Optimization and Applications, 2020, vol. 76, issue 1, No 5, 155-199

Abstract: Abstract 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.

Keywords: Bilinear boundary control; Identification of Robin parameter; Finite element error estimates; Postprocessing approach (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10589-020-00171-5

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