Nonlinear Continuous Data Assimilation

Adam Larios; Yuan Pei

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arXiv · 1703.03546

Nonlinear Continuous Data Assimilation

Adam Larios·Yuan Pei

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Abstract

We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Olson, and Titi (AOT). As a proof-of-concept for these models, we computationally investigate these algorithms in the context of the 1D Kuramoto-Sivashinsky equation. We observe that the nonlinear models experience super-exponential convergence in time, and converge to machine precision significantly faster than the linear AOT algorithm in our tests.

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Adam Larios, Yuan Pei. 2017-03-10. Nonlinear Continuous Data Assimilation. https://arxiv.org/abs/1703.03546

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