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Spacetime finite element methods for control problems subject to the wave equation

Burman, Erik; Feizmohammadi, Ali; Münch, Arnaud; Oksanen, Lauri; (2023) Spacetime finite element methods for control problems subject to the wave equation. ESAIM: Control, Optimisation and Calculus of Variations , 29 , Article 41. 10.1051/cocv/2023028. Green open access

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Abstract

We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the computational method. The proofs are based on the regularity properties of the control given by the Hilbert Uniqueness Method, together with the stability properties of the numerical scheme. Numerical experiments illustrate the results.

Type: Article
Title: Spacetime finite element methods for control problems subject to the wave equation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1051/cocv/2023028
Publisher version: https://doi.org/10.1051/cocv/2023028
Language: English
Additional information: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: Wave equation, control, finite element method, space time, stabilisation
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10172558
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