Burman, E;
Nechita, M;
Oksanen, L;
(2019)
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime.
Numerische Mathematik
10.1007/s00211-019-01087-x.
(In press).
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Abstract
The numerical approximation of an inverse problem subject to the convection–diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are of a form suitable for use in numerical analysis and with explicit dependence on the Péclet number. A stabilized finite element method is then proposed and analysed. An upper bound on the condition number is first derived. Combining the stability estimates on the continuous problem with the numerical stability of the method, we then obtain error estimates in local H1 - or L2 -norms that are optimal with respect to the approximation order, the problem’s stability and perturbations in data. The convergence order is the same for both norms, but the H1 -estimate requires an additional divergence assumption for the convective field. The theory is illustrated in some computational examples.
| Type: | Article |
|---|---|
| Title: | A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00211-019-01087-x |
| Publisher version: | https://doi.org/10.1007/s00211-019-01087-x |
| Language: | English |
| Additional information: | Copyright information © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| 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.ucl.ac.uk/id/eprint/10086169 |
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