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

被引：0
作者：
Max Winkler
机构：
[1] Technische Universität Chemnitz,Faculty of Mathematics
来源：
Computational Optimization and Applications | 2020年 / 76卷
关键词：
Bilinear boundary control; Identification of Robin parameter; Finite element error estimates; Postprocessing approach;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：155 / 199
页数：44
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