Error estimates for the finite element approximation of bilinear boundary control problems
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arXiv
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866909434610974720 |
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| author | Winkler, Max |
| author_facet | Winkler, Max |
| contents | 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. To this end, necessary and sufficient optimality conditions are derived and several discretization approaches for the numerical solution 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_03612 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Error estimates for the finite element approximation of bilinear boundary control problems Winkler, Max Numerical Analysis 35J05, 35Q93, 49J20, 65N21, 65N30 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. To this end, necessary and sufficient optimality conditions are derived and several discretization approaches for the numerical solution 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. |
| title | Error estimates for the finite element approximation of bilinear boundary control problems |
| topic | Numerical Analysis 35J05, 35Q93, 49J20, 65N21, 65N30 |
| url | https://arxiv.org/abs/1901.03612 |