Deferred correction method for the continuous data assimilation model

This paper presents a numerical assessment of a continuous data assimilation (CDA) model for incompressible Navier–Stokes equations. The proposed model employs the deferred correction method, which is an approach to increase temporal accuracy. What makes this work valuable is the necessity of obtaining high temporal accuracy results, which is only possible with the deferred correction method for some problems, e.g., the decoupling of the atmosphere–ocean interaction problem (Temam et al., 1993 [1]; Erkmen et al., 2018). The scheme involves incorporating a nudging term into a traditional deferred correction scheme in order to calibrate a model to match coarse mesh or spatial observations at a larger scale. We present stability, long time stability, and convergence results of the scheme in detail. We also illustrate some numerical experiments to validate and reinforce the theoretical results.