# 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…

## 125 Citations

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Motivated by the presence of a finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, we present a continuous…

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Motivated by the presence of a finite number of determining parameters (degrees of freedom) such as modes, nodes and local spatial averages for dissipative dynamical systems, we present a continuous…

Continuous data assimilation with stochastically noisy data

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We analyse the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of…

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A continuous data assimilation algorithm for three-dimensional viscous hydrodynamic models that provides conditions on the finite-dimensional spatial resolution of the collected data sufficient to guarantee that the approximating solution, which is obtained from this collected data, converges to the unknown reference solution over time.

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Author(s): Foias, Ciprian; Mondaini, Cecilia F; Titi, Edriss S | Abstract: We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes…

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An interpolation operator designed for use with continuous data assimilation of evolution equations that are discretized spatially with the finite element method is introduced and proved to have sufficient stability and accuracy properties.

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Uniform-in-time estimates are obtained for the error between the numerical approximation given by the postprocessing Galerkin method and the reference solution corresponding to the measurements from a coarse spatial mesh.

Title Abridged continuous data assimilation for the 2 D Navier-Stokes equations utilizing measurements of only one component of the velocity field Permalink

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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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