| Contents |
| We analyze the performance of a data-assimilation method based on a
linear feedback control when used with observational data that
contains measurement errors. Our model problem consists of dynamics
governed by the two-dimension incompressible Navier--Stokes
equations, observational measurements given by finite volume
elements or nodal points of the velocity field and measurement
errors which are represented by stochastic noise. Under these
assumptions, the data-assimilation algorithm consists of a system of
stochastically forced Navier--Stokes equations. The main result of
this paper gives conditions on the observation density which
guarantee that the expected value of the approximating solution will
converge to the actual solution to within a factor related to the
variance of the noise in the measurements. |
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