31 citations · 57 across the 7 of their papers we have counts for
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Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
Adam Larios, Elizabeth Carlson
We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations. Moreo…
Parameter Recovery and Sensitivity Analysis for the 2D Navier-Stokes Equations Via Continuous Data Assimilation
Elizabeth Carlson, Joshua Hudson, Adam Larios
We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi (AOT) in the context of an unknown Reynolds number. We determine the large-time error between…
Continuous Data Assimilation with a Moving Cluster of Data Points for a Reaction Diffusion Equation: A Computational Study
Adam Larios, Collin Victor
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as tim…
Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data
Adam Larios, Yuan Pei
We propose a data assimilation algorithm for the 2D Navier-Stokes equations, based on the Azouani, Olson, and Titi (AOT) algorithm, but applied to the 2D Navier-Stokes-Voigt equati…
Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations
Adam Larios, Yuan Pei, Leo Rebholz
The velocity-vorticity formulation of the 3D Navier-Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose…
Nonlinear Continuous Data Assimilation
Adam Larios, Yuan Pei
We introduce three new nonlinear continuous data assimilation algorithms. These models are compared with the linear continuous data assimilation algorithm introduced by Azouani, Ol…