Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations

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https://www.aimsciences.org/article/doi/10.3934/dcds.2023078

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https://doi.org/10.3934/dcds.2023078
 http://hdl.handle.net/11603/30262

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UMBC Mathematics and Statistics Department
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https://orcid.org/0000-0001-8594-0568

Date

2023-11

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journal articles
preprints
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Citation of Original Publication

Animikh Biswas, Zachary Bradshaw, Michael Jolly. Convergence of a mobile data assimilation scheme for the 2D Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2023, 43(11): 4042-4068. doi: 10.3934/dcds.2023078

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This is the version of the article before peer review or editing, as submitted by an author to Discrete and Continuous Dynamic Systems (https://www.aimsciences.org/dcds). AIMS is not responsible for any errors or omissions in this version of the manuscript, or any version derived from it.

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Abstract

We introduce a localized version of the nudging data assimilation algorithm for the periodic 2D Navier-Stokes equations in which observations are confined (i.e., localized) to a window that moves across the entire domain along a predetermined path at a given speed. We prove that, if the movement is fast enough, then the algorithm perfectly synchronizes with a reference solution. The analysis suggests an informed scheme in which the subdomain moves according to a region where the error is dominant is optimal. Numerical simulations are presented that compare the efficacy of movement that follows a regular pattern, one guided by the dominant error, and one that is random.