Nonlinear Continuous Data Assimilation

• DOI: 10.48550/arxiv.1703.03546
• Publication Date: 2024-01-01
• Authors: Larios, Adam; Pei, Yuan
• Keywords: Mathematics - Analysis of PDEs; FOS: Mathematics; 35Q35, 35Q86, 65Z05; 0101 mathematics; 01 natural sciences; Analysis of PDEs (math.AP)

15 pages, 19 figures<br/>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.<br/>