Burman, Erik;
Garg, Deepika;
Preuss, Janosch;
(2024)
Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation.
ESAIM: Mathematical Modelling and Numerical Analysis
, 58
(1)
pp. 223-245.
10.1051/m2an/2023106.
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Abstract
In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier–Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.
| Type: | Article |
|---|---|
| Title: | Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an/2023106 |
| Publisher version: | https://doi.org/10.1051/m2an/2023106 |
| Language: | English |
| Additional information: | © The authors. Published by EDP Sciences, SMAI 2024 Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Linearized Navier–Stokes’ equations, data assimilation, stabilized finite element methods, error estimates |
| 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/10188004 |
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