Nonlinear Continuous Data Assimilation
Analysis of PDEs
2017-03-13 v1
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.
Cite
@article{arxiv.1703.03546,
title = {Nonlinear Continuous Data Assimilation},
author = {Adam Larios and Yuan Pei},
journal= {arXiv preprint arXiv:1703.03546},
year = {2017}
}
Comments
15 pages, 19 figures