An a posteriori error analysis for an optimal control problem with point sources
We propose and analyze a reliable and efficient a posteriori error estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposed a posteriori error estimator is...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2018
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| Online Access: | https://eprints.nottingham.ac.uk/55774/ |
| _version_ | 1848799212784844800 |
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| author | Allendes, Alejandro Otárola, Enrique Rankin, Richard Salgado, Abner J. |
| author_facet | Allendes, Alejandro Otárola, Enrique Rankin, Richard Salgado, Abner J. |
| author_sort | Allendes, Alejandro |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We propose and analyze a reliable and efficient a posteriori error estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposed a posteriori error estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the devised a posteriori error estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform. © 2018 EDP Sciences, SMAI. |
| first_indexed | 2025-11-14T20:32:05Z |
| format | Article |
| id | nottingham-55774 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:32:05Z |
| publishDate | 2018 |
| publisher | EDP Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-557742019-01-02T13:48:16Z https://eprints.nottingham.ac.uk/55774/ An a posteriori error analysis for an optimal control problem with point sources Allendes, Alejandro Otárola, Enrique Rankin, Richard Salgado, Abner J. We propose and analyze a reliable and efficient a posteriori error estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposed a posteriori error estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the devised a posteriori error estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform. © 2018 EDP Sciences, SMAI. EDP Sciences 2018-09-01 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/55774/1/Point_Sources.pdf Allendes, Alejandro, Otárola, Enrique, Rankin, Richard and Salgado, Abner J. (2018) An a posteriori error analysis for an optimal control problem with point sources. ESAIM: Mathematical Modelling and Numerical Analysis, 52 (5). pp. 1617-1650. ISSN 1290-3841 http://dx.doi.org/10.1051/m2an/2018010 doi:10.1051/m2an/2018010 doi:10.1051/m2an/2018010 |
| spellingShingle | Allendes, Alejandro Otárola, Enrique Rankin, Richard Salgado, Abner J. An a posteriori error analysis for an optimal control problem with point sources |
| title | An a posteriori error analysis for an optimal control problem with point sources |
| title_full | An a posteriori error analysis for an optimal control problem with point sources |
| title_fullStr | An a posteriori error analysis for an optimal control problem with point sources |
| title_full_unstemmed | An a posteriori error analysis for an optimal control problem with point sources |
| title_short | An a posteriori error analysis for an optimal control problem with point sources |
| title_sort | a posteriori error analysis for an optimal control problem with point sources |
| url | https://eprints.nottingham.ac.uk/55774/ https://eprints.nottingham.ac.uk/55774/ https://eprints.nottingham.ac.uk/55774/ |