Burman, E;
(2017)
A stabilized nonconforming finite element method for the elliptic Cauchy problem.
Mathematics of Computation
, 86
(303)
pp. 75-96.
10.1090/mcom/3092.
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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. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data on the estimates is investigated. The recently derived framework from \cite{Bu13,Bu14} is extended to include the case of nonconforming approximation spaces and we show that the use of such spaces allows us to reduce the amount of stabilization necessary for convergence, even in the case of ill-posed problems.
| Type: | Article |
|---|---|
| Title: | A stabilized nonconforming finite element method for the elliptic Cauchy problem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/mcom/3092 |
| Publisher version: | https://doi.org/10.1090/mcom/3092 |
| Language: | English |
| Additional information: | First published in Mathematics of Computation in 2016, published by the American Mathematical Society. Copyright © the American Mathematical Society 2016. |
| 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-pp.ucl.ac.uk/id/eprint/1476743 |
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