Data Assimilation with Higher Order Finite Element Interpolants

TL;DR

This paper investigates a nudging data assimilation algorithm using higher order finite element interpolants, demonstrating improved accuracy over first order methods through numerical experiments on 2D Navier-Stokes flows and providing convergence proofs.

Contribution

It introduces and analyzes the use of higher order finite element interpolants in nudging data assimilation, showing their advantages over first order methods.

Findings

Second order interpolation outperforms first order in numerical experiments.

Convergence of the nudged solution to the reference solution is proven.

Trade-offs exist in the estimates for higher order interpolating operators.

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.