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Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the navier-stokes equations

Accepted version
Peer-reviewed

Type

Article

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Authors

García-Archilla, B 
Novo, J 
Titi, ES 

Abstract

In this paper we analyze a finite element method applied to a continuous downscaling data assimilation algorithm for the numerical approximation of the two and three dimensional Navier-Stokes equations corresponding to given measurements on a coarse spatial scale. For representing the coarse mesh measurements we consider different types of interpolation operators including a Lagrange interpolant. We obtain uniform-in-time estimates for the error between a finite element approximation and the reference solution corresponding to the coarse mesh measurements. We consider both the case of a plain Galerkin method and a Galerkin method with grad-div stabilization. For the stabilized method we prove error bounds in which the constants do not depend on inverse powers of the viscosity. Some numerical experiments illustrate the theoretical results.

Description

Keywords

math.NA, math.NA, math.AP, physics.ao-ph, physics.flu-dyn, 35Q30, 65M12, 65M15, 65M20, 65M60, 65M70, 76B75

Journal Title

SIAM Journal on Numerical Analysis

Conference Name

Journal ISSN

0036-1429
1095-7170

Volume Title

58

Publisher

Society for Industrial & Applied Mathematics (SIAM)