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.

翻译：研究了使用更高顺序限制要素内插操作器的裸化数据同化算法的功效,对2D Navier-Stokes等式的两个实例进行了数字实验:在废旧的剪切流和在圆盘中以离中空腔强制流。在两种情形中,粗谷物数据的第二顺序内插都显示优于第一顺序内插。对直接数字参考解决方案的推力解决办法的趋同得到了证明。分析表明,较高顺序内插操作器估计数的权衡是权衡的。