Burman, Erik;
Nechita, Mihai;
Oksanen, Lauri;
(2022)
A stabilized finite element method for inverse problems subject to the convection–diffusion equation. II: convection-dominated regime.
Numerische Mathematik
, 150
pp. 769-801.
10.1007/s00211-022-01268-1.
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Abstract
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection–diffusion equations and extend our previous analysis in Burman et al. (Numer. Math. 144:451–477, 2020) to the convection-dominated regime. Slightly adjusting the stabilized finite element method proposed for dominant diffusion, we draw upon a local error analysis to obtain quasi-optimal convergence along the characteristics of the convective field through the data set. The weight function multiplying the discrete solution is taken to be Lipschitz continuous and a corresponding super approximation result (discrete commutator property) is proven. The effect of data perturbations is included in the analysis and we conclude the paper with some numerical experiments.
| Type: | Article |
|---|---|
| Title: | A stabilized finite element method for inverse problems subject to the convection–diffusion equation. II: convection-dominated regime |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00211-022-01268-1 |
| Publisher version: | https://doi.org/10.1007/s00211-022-01268-1 |
| Language: | English |
| Additional information: | 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 > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS UCL 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/10143729 |
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