Data Assimilation with Higher Order Finite Element Interpolants
Numerical Analysis
2021-08-10 v1 Numerical Analysis
Dynamical Systems
Computational Physics
Fluid Dynamics
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.
Cite
@article{arxiv.2108.03631,
title = {Data Assimilation with Higher Order Finite Element Interpolants},
author = {Michael S. Jolly and Ali Pakzad},
journal= {arXiv preprint arXiv:2108.03631},
year = {2021}
}
Comments
18 pages, 10 figures, 1 table