Data assimilation with higher order finite element interpolants

摘要

The 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