In this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element method. First conditional stability estimates are derived for which, under a convexity assumption on the geometry, the constants grow at most linearly in the wave number. Then these estimates are used to obtain error bounds for the finite element method that are explicit with respect to the wave number. Some numerical illustrations are given.


Erik Burman
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom

Mihai Nechita
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom

Lauri Oksanen
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom


Helmholtz equation; unique continuation; Finite Element method; wave number explicit; conditional Hölder stability.

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E. Burman, M. Nechita, L. Oksanen, Unique continuation for the Helmholtz equation using stabilized finite element methods, J. Math. Pures Appl., 2019 (to appear)
DOI: 10.1016/j.matpur.2018.10.003


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Journal de Mathématiques Pures et Appliquées

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