We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …

This paper considers continuous data assimilation (CDA) in partial differential equation
(PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove …

This article studies the interrelation between the determining modes property in the two-
dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the …

This article studies the intimate relationship between two filtering algorithms for continuous
data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context …

This paper considers improving the Picard and Newton iterative solvers for the Navier–
Stokes equations in the setting where data measurements or solution observations are …

Data assimilation combines (imperfect) knowledge of a flow's physical laws with (noisy, time-
lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow …

The main objective of this paper is to consider a continuous data assimilation algorithm for
the three-dimensional planetary geostrophic model in the case that the observable …

We introduce three new nonlinear continuous data assimilation algorithms. These models
are compared with the linear continuous data assimilation algorithm introduced by Azouani …

The efficiency of a nudging data assimilation algorithm using higher order finite element
interpolating operators is studied. Numerical experiments are presented for the 2D Navier …

This article is concerned with the problem of determining an unknown source of non-
potential, external time-dependent perturbations of an incompressible fluid from large-scale …