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Data assimilation finite element method for the linearized Navier-Stokes equations in the low Reynolds regime

Boulakia, M; Burman, E; Fernandez, MA; Voisembert, C; (2020) Data assimilation finite element method for the linearized Navier-Stokes equations in the low Reynolds regime. Inverse Problems 10.1088/1361-6420/ab9161. (In press). Green open access

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Abstract

In this paper we are interested in designing and analyzing a finite element data assimilation method for laminar steady flow described by the linearized incompressible Navier-Stokes equation. We propose a weakly consistent stabilized finite element method which reconstructs the whole fluid flow from velocity measurements in a subset of the computational domain. Using the stability of the continuous problem in the form of a three balls inequality, we derive quantitative local error estimates for the velocity. Numerical simulations illustrate these convergences properties and we finally apply our method to the flow reconstruction in a blood vessel.

Type: Article
Title: Data assimilation finite element method for the linearized Navier-Stokes equations in the low Reynolds regime
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/ab9161
Publisher version: http://dx.doi.org/10.1088/1361-6420/ab9161
Language: English
Additional information: As the Version of Record of this article is going to be/has been published on a gold open access basis under a CC BY 3.0 licence, this Accepted Manuscript is available for reuse under a CC BY 3.0 licence immediately. Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission may be required. All third party content is fully copyright protected, and is not published on a gold open access basis under a CC BY licence, unless that is specifically stated in the figure caption in the Version of Record.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/10097298
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