Nonlinear Continuous Data Assimilation

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.

15 pages, 19 figures

References in corpus (1)

• Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone