Global in time stability and accuracy of IMEX-FEM data assimilation schemes for the Navier-Stokes equations

Abstract

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.

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Cited by in corpus (8)

• Continuous Data Assimilation Reduced Order Models of Fluid Flow
• The Bleeps, the Sweeps, and the Creeps: Convergence Rates for Dynamic Observer Patterns via Data Assimilation for the 2D Navier-Stokes Equations
• Mesh-Free Interpolant Observables for Continuous Data Assimilation
• Data Assimilation in Large-Prandtl Rayleigh-Bénard Convection from Thermal Measurements
• Continuous Data Assimilation for the Double-Diffusive Natural Convection
• Error analysis of proper orthogonal decomposition data assimilation schemes for the Navier-Stokes equations
• Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
• Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data