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Consider a continuous dynamical system for which partial information aboutits current state is observed at a sequence of discrete times. Discrete dataassimilation inserts these observational measurements of the referencedynamical system into an approximate solution by means of an impulsive forcing.In this way the approximating solution is coupled to the reference solution ata discrete sequence of points in time. This paper studies discrete dataassimilation for the Lorenz equations and the incompressible two-dimensionalNavier--Stokes equations. In both cases we obtain bounds on the time interval hbetween subsequent observations which guarantee the convergence of theapproximating solution obtained by discrete data assimilation to the referencesolution.

Discrete Data Assimilation in the Lorenz and 2D Navier--Stokes Equations