Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations
Provides rigorous stability and accuracy guarantees for a data assimilation technique in computational fluid dynamics, though the analysis is incremental and builds on existing methods.
The paper proves long-time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations, with numerical tests confirming theoretical restrictions on time step and assimilation parameters.
We study numerical schemes for incompressible Navier-Stokes equations using IMEX temporal discretizations, finite element spacial discretizations, and equipped with continuous data assimilation (a technique recently developed by Azouani, Olson, and Titi in 2014). We analyze stability and accuracy of the proposed methods, and are able to prove well-posedness, long time stability, and long time accuracy estimates, under restrictions of the time step size and data assimilation parameter. We give results for several numerical tests that illustrate the theory, and show that, for good results, the choice of discretization parameter and element choices can be critical.