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A finite element data assimilation method for the wave equation

Burman, E; Feizmohammadi, A; Oksanen, L; (2020) A finite element data assimilation method for the wave equation. Mathematics of Computation , 89 (2020) 10.1090/mcom/3508. Green open access

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Abstract

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions are used for the approximation in space and backward differentiation is used in time. Stabilizing terms are added on the discrete level. The design of these terms is driven by numerical stability and the stability of the continuous problem, with the objective of minimizing the computational error. Error estimates are then derived that are optimal with respect to the approximation properties of the numerical scheme and the stability properties of the continuous problem. The effects of discretizing the (smooth) domain boundary and other perturbations in data are included in the analysis.

Type: Article
Title: A finite element data assimilation method for the wave equation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1090/mcom/3508
Publisher version: https://doi.org/10.1090/mcom/3508
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/10086084
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