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A stabilized nonconforming finite element method for the elliptic Cauchy problem


Author: Erik Burman
Journal: Math. Comp. 86 (2017), 75-96
MSC (2010): Primary 65N12, 65N15, 65N20, 65N21, 65N30
DOI: https://doi.org/10.1090/mcom/3092
Published electronically: April 4, 2016
MathSciNet review: 3557794
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Abstract: In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. The recently derived framework from previous works of the author is extended to include the case of a nonconforming approximation space. We show that the use of such a space allows us to reduce the amount of stabilization necessary for convergence, even in the case of ill-posed problems. We derive error estimates using conditional stability estimates in the $ L^2$-norm.


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Additional Information

Erik Burman
Affiliation: Department of Mathematics, University College London, London, UK-WC1E 6BT, United Kingdom
Email: e.burman@ucl.ac.uk

DOI: https://doi.org/10.1090/mcom/3092
Received by editor(s): June 17, 2014
Received by editor(s) in revised form: March 20, 2015, and June 8, 2015
Published electronically: April 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society