A discrete data assimilation scheme for the solutions of the 2D Navier-Stokes equations and their statistics

Abstract

We adapt a previously introduced continuous in time data assimilation (downscaling) algorithm for the 2D Navier-Stokes equations to the more realistic case when the measurements are obtained discretely in time and may be contaminated by systematic errors. Our algorithm is designed to work with a general class of observables, such as low Fourier modes and local spatial averages over finite volume elements. Under suitable conditions on the relaxation (nudging) parameter, the spatial mesh resolution and the time step between successive measurements, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to a term which depends on the size of the errors. A stationary statistical analysis of our discrete data assimilation algorithm is also provided.

References in corpus (4)

• Continuous Data Assimilation for the 2D Bénard Convection through Velocity Measurements Alone
• Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model
• Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field
• Downscaling the 2D Benard Convection Equations Using Continuous Data Assimilation

Cited by in corpus (3)

• Mesh-Free Interpolant Observables for Continuous Data Assimilation
• Postprocessing Galerkin method applied to a data assimilation algorithm: a uniform in time error estimate
• Data Assimilation in Large-Prandtl Rayleigh-Bénard Convection from Thermal Measurements