2000 character limit reached
Data Assimilation with Higher Order Finite Element Interpolants (2108.03631v1)
Published 8 Aug 2021 in math.NA, cs.NA, math.DS, physics.comp-ph, and physics.flu-dyn
Abstract: 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.