Adaptive finite element method for an unregularized semilinear optimal control problem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915276270862336 |
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| author | Fuica, Francisco Jork, Nicolai |
| author_facet | Fuica, Francisco Jork, Nicolai |
| contents | We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational discretization approach. For this solution technique, we design an a posteriori error estimator that accounts for the discretization of the state and adjoint equations, and prove, under suitable local growth conditions of optimal controls, reliability and efficiency properties of such error estimator. A simple adaptive strategy based on the devised estimator is designed and its performance is illustrated with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive finite element method for an unregularized semilinear optimal control problem Fuica, Francisco Jork, Nicolai Optimization and Control Numerical Analysis 35J61, 49M25, 65N15, 65N30 We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational discretization approach. For this solution technique, we design an a posteriori error estimator that accounts for the discretization of the state and adjoint equations, and prove, under suitable local growth conditions of optimal controls, reliability and efficiency properties of such error estimator. A simple adaptive strategy based on the devised estimator is designed and its performance is illustrated with numerical examples. |
| title | Adaptive finite element method for an unregularized semilinear optimal control problem |
| topic | Optimization and Control Numerical Analysis 35J61, 49M25, 65N15, 65N30 |
| url | https://arxiv.org/abs/2505.04439 |