| Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
|---|---|---|
| Page(s) | 223 - 245 | |
| DOI | https://doi.org/10.1051/m2an/2023106 | |
| Published online | 16 February 2024 | |
Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation
Department of Mathematics, University College London, London WC1E 6BT, UK
* Corresponding author: d.garg@ucl.ac.uk
Received:
12
December
2022
Accepted:
20
December
2023
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.
Mathematics Subject Classification: 76D05 / 35R30 / 76M10
Key words: Linearized Navier–Stokes’ equations / data assimilation / stabilized finite element methods / error estimates
© The authors. Published by EDP Sciences, SMAI 2024
This 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.
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