| Abstract: |
| We consider a feedback-control (nudging) approach for data assimilation that works for a general class of dissipative dynamical systems and observables. As a model example, we consider the 2D incompressible Navier-Stokes equations (NSE). Our purpose is to present an estimate of the error between a numerical approximation of the solution to the nudging equation and a reference solution of the 2D NSE, representing the truth. We consider a spatial discretization given by the Postprocessing Galerkin method and two types of implicit Euler schemes for the time discretization: fully implicit and semi-implicit. Our results show that the time-discrete schemes are unconditionally stable and the error estimates are uniform in time. This is based on joint works with H. Ibdah and E. S. Titi. |
|