  The efficacy of a nudging data assimilation algorithm using higher order
finite element interpolating operators is studied. Numerical experiments are
presented for the 2D Navier-Stokes equations in two cases: shear flow in an
annulus and a forced flow in a disk with an off-center cavity. In both cases
second order interpolation of coarse-grain data is shown to outperform first
order interpolation. Convergence of the nudged solution to that of a direct
numerical reference solution is proved. The analysis points to a trade-off in
the estimates for higher order interpolating operators.
