Nonlinear Continuous Data Assimilation
arXiv:1703.03546
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
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- Continuous data assimilation for the 3D primitive equations of the ocean
- Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
- Parameter Recovery and Sensitivity Analysis for the 2D Navier-Stokes Equations Via Continuous Data Assimilation