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