Continuous Data Assimilation Using General Interpolant Observables

@article{Azouani2014ContinuousDA,
  title={Continuous Data Assimilation Using General Interpolant Observables},
  author={Abderrahim Azouani and Eric Olson and Edriss S. Titi},
  journal={Journal of Nonlinear Science},
  year={2014},
  volume={24},
  pages={277-304}
}
We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible two-dimensional Navier–Stokes equations. These ideas are motivated by the fact that dissipative dynamical systems possess finite numbers of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages which govern their long-term… 
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We introduce a continuous data assimilation (downscaling) algorithm for the two-dimensional Navier-Stokes equations employing coarse mesh measurements of only one component of the velocity field.
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