An a posteriori error analysis for an optimal control problem with point sources

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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

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Abstract

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.

Item Type: Article
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.1051/m2an/2018010
Depositing User: QIU, Lulu
Date Deposited: 02 Jan 2019 13:48
Last Modified: 02 Jan 2019 13:48
URI: https://eprints.nottingham.ac.uk/id/eprint/55774

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