Volume 29, 2023
|Number of page(s)||40|
|Published online||09 June 2023|
Spacetime finite element methods for control problems subject to the wave equation
Department of Mathematics, University College London,
London WC1E 6BT,
2 Department of Mathematics, University of Toronto, 3359 Mississauga Road Deerfield Hall, Mississauga, Ontario, Canada L5L 1C6
3 Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
4 Department of Mathematics and Statistics, University of Helsinki, P.O 68, 00014 University of Helsinki, Finland
* Corresponding author: firstname.lastname@example.org
Accepted: 11 April 2023
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.
Mathematics Subject Classification: 35L05 / 93-08 / 65M12 / 65M60
Key words: Wave equation / control / finite element method / space time / stabilisation
© The authors. Published by EDP Sciences, SMAI 2023
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