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.

## Abstract

## Authors

**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

## Keywords

## Paper coordinates

E. Burman, M. Nechita, L. Oksanen, *Unique continuation for the Helmholtz equation using stabilized finite element methods, *J. Math. Pures Appl., **129 **(2019), pp. 1-22.*
*DOI: 10.1016/j.matpur.2018.10.003

## About this paper

##### Journal

Journal de Mathématiques Pures et Appliquées

##### Publisher Name

Elsevier

##### Print ISSN

0021-7824

##### Online ISSN

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