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

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 prope...

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Bibliographic Details
Published inESAIM. Control, optimisation and calculus of variations Vol. 29; p. 41
Main Authors Burman, Erik, Feizmohammadi, Ali, Münch, Arnaud, Oksanen, Lauri
Format Journal Article
LanguageEnglish
Published 2023
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Summary: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2023028