A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908406480109568 |
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| author | Winkler, Max Yücel, Hamdullah |
| author_facet | Winkler, Max Yücel, Hamdullah |
| contents | The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error estimates are derived for the control variable in $L^2(\partial \mathcal D)$-norm and state variable in $L^2(Ω\times\mathcal D)$-norm. To solve large linear systems, appropriate preconditioners are proposed for both unconstrained and constrained scenarios. To illustrate the validity and efficiency of the proposed approaches, some numerical experiments are performed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data Winkler, Max Yücel, Hamdullah Optimization and Control Numerical Analysis 35R60, 65K15, 65N30, 93E20 G.1.8 The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error estimates are derived for the control variable in $L^2(\partial \mathcal D)$-norm and state variable in $L^2(Ω\times\mathcal D)$-norm. To solve large linear systems, appropriate preconditioners are proposed for both unconstrained and constrained scenarios. To illustrate the validity and efficiency of the proposed approaches, some numerical experiments are performed. |
| title | A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data |
| topic | Optimization and Control Numerical Analysis 35R60, 65K15, 65N30, 93E20 G.1.8 |
| url | https://arxiv.org/abs/2506.11479 |