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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.<\/jats:p>","DOI":"10.1007\/s10589-020-00171-5","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T23:02:15Z","timestamp":1581116535000},"page":"155-199","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Error estimates for the finite element approximation of bilinear boundary control problems"],"prefix":"10.1007","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5292-2280","authenticated-orcid":false,"given":"Max","family":"Winkler","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"171_CR1","volume-title":"Anisotropic Finite Elements: Local Estimates and Applications","author":"Th Apel","year":"1999","unstructured":"Apel, Th: Anisotropic Finite Elements: Local Estimates and Applications. 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