  In this paper we propose the use of a continuous data assimilation algorithm
for miscible flow models in a porous medium. In the absence of initial
conditions for the model, observed sparse measurements are used to generate an
approximation to the true solution. Under certain assumption of the sparse
measurements and their incorporation into the algorithm it can be shown that
the resulting approximate solution converges to the true solution at an
exponential rate as time progresses. Various numerical examples are considered
in order to validate the suitability of the algorithm.

Numerical Analysis;Numerical Analysis