AbstractThe efficiency 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 three cases: shear flow in an annulus, a forced flow in a disk with an off‐center cavity, and a forced flow in a box all satisfying Dirichlet boundary conditions. In all three 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