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Discrete data assimilation algorithm for the three-dimensional Leray-$\alpha $ model

Volume 66 / 2018

Cung The Anh, Bui Huy Bach Bulletin Polish Acad. Sci. Math. 66 (2018), 143-156 MSC: 35Q35, 37C50, 76B75, 93C20. DOI: 10.4064/ba8162-11-2018 Published online: 19 December 2018

Abstract

We study the data assimilation algorithm for the three-dimensional Leray-$\alpha $ model when the measurements are obtained discretely in time and may be contaminated by systematic errors. Under suitable conditions on the relaxation (nudging) parameter, the spatial mesh resolution, and the time step between successive measurements, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to a term which depends on the size of the errors.

Authors

  • Cung The AnhDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
    e-mail
  • Bui Huy BachDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
    e-mail

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