Nonlinear continuous data assimilation
Copyright policy )Nonlinear continuous data assimilation
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
- University of Nebraska System United States
PDEs in connection with control and optimization, Kuramoto-Sivashinsky equation, Higher-order parabolic systems, Control/observation systems governed by partial differential equations, Synchronization of solutions to ordinary differential equations, 35Q35, 35Q86, 65Z05, nonlinear data assimilation, feedback control, Mathematics - Analysis of PDEs, nudging, FOS: Mathematics, Azouani-Olson-Titi, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, Analysis of PDEs (math.AP)
PDEs in connection with control and optimization, Kuramoto-Sivashinsky equation, Higher-order parabolic systems, Control/observation systems governed by partial differential equations, Synchronization of solutions to ordinary differential equations, 35Q35, 35Q86, 65Z05, nonlinear data assimilation, feedback control, Mathematics - Analysis of PDEs, nudging, FOS: Mathematics, Azouani-Olson-Titi, Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations, Analysis of PDEs (math.AP)
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