Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONTINUOUS DATA ASSIMILATION FOR THE THREE-DIMENSIONAL SIMPLIFIED BARDINA MODEL UTILIZING MEASUREMENTS OF ONLY TWO COMPONENTS OF THE VELOCITY FIELD

  • Anh, Cung The (Department of Mathematics Hanoi National University of Education) ;
  • Bach, Bui Huy (Department of Mathematics Hanoi National University of Education)
  • Received : 2019.05.18
  • Accepted : 2020.08.31
  • Published : 2021.01.01
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Abstract

We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, 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 zero.

Keywords

Acknowledgement

The authors would like to thank the reviewers for the helpful comments and suggestions, which improved the presentation of the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.303.

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