Burman, E;
Feizmohammadi, A;
Oksanen, L;
(2020)
A Fully Discrete Numerical Control Method for the Wave Equation.
SIAM Journal on Control and Optimization
, 58
(3)
pp. 1519-1546.
10.1137/19M1249424.
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Abstract
We present a fully discrete finite element method for the interior null controllability problem subject to the wave equation. For the numerical scheme, piecewise affine continuous elements in space and finite differences in time are considered. We show that if the sharp geometric control condition holds, our numerical scheme yields the optimal rate of convergence with respect to the space-time mesh parameter. The approach is based on the design of stabilization terms for the discrete scheme with the goal of minimizing the computational error.
| Type: | Article |
|---|---|
| Title: | A Fully Discrete Numerical Control Method for the Wave Equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/19M1249424 |
| Publisher version: | https://doi.org/10.1137/19M1249424 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | wave equation, control, numerical analysis, finite element method, stabilization |
| 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.ucl.ac.uk/id/eprint/10100593 |
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