  In this paper we introduce and analyze an algorithm for continuous data
assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D
BFeD) model of porous media. This model is believed to be accurate when the
flow velocity is too large for Darcy's law to be valid, and additionally the
porosity is not too small. The algorithm is inspired by ideas developed for
designing finite-parameters feedback control for dissipative systems. It aims
to obtaining improved estimates of the state of the physical system by
incorporating deterministic or noisy measurements and observations.
Specifically, the algorithm involves a feedback control that nudges the large
scales of the approximate solution toward those of the reference solution
associated with the spatial measurements. In the first part of the paper, we
present few results of existence and uniqueness of weak and strong solutions of
the 3D BFeD system. The second part is devoted to the setting and convergence
analysis of the data assimilation algorithm.
