eprintid: 10188004 rev_number: 8 eprint_status: archive userid: 699 dir: disk0/10/18/80/04 datestamp: 2024-02-27 16:33:12 lastmod: 2024-02-27 16:33:12 status_changed: 2024-02-27 16:33:12 type: article metadata_visibility: show sword_depositor: 699 creators_name: Burman, Erik creators_name: Garg, Deepika creators_name: Preuss, Janosch title: Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 keywords: Linearized Navier–Stokes’ equations, data assimilation, stabilized finite element methods, error estimates note: © 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. 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. date: 2024-02-16 date_type: published publisher: EDP Sciences official_url: https://doi.org/10.1051/m2an/2023106 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2252202 doi: 10.1051/m2an/2023106 lyricists_name: Burman, Erik lyricists_name: Garg, Deepika lyricists_name: Preuss, Janosch lyricists_id: ENBUR31 lyricists_id: DGARG60 lyricists_id: JPREU53 actors_name: Flynn, Bernadette actors_id: BFFLY94 actors_role: owner full_text_status: public publication: ESAIM: Mathematical Modelling and Numerical Analysis volume: 58 number: 1 pagerange: 223-245 issn: 2822-7840 citation: 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 <https://doi.org/10.1051/m2an%2F2023106>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10188004/1/m2an220265.pdf