  The first aim of this work is to construct a Finite Elements model for
quasi-geostrophic equation. This model is analyzed through FEniCS interface. As
a second purpose, it shows the potential of the control theory to treat Data
Assimilation large scale problems. In section one the finite element
approximation of the quasi-geostrophic model is described. In section two some
numerical results on different domains are shown. In section three a comparison
between Navier Stokes model and quasi-geostrophic one is discussed. Last
section is dedicated to a more complex data assimilation/control problem based
on quasi-geostrophic equations, to test possible developments and improvements.
