Article
Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations
Author/s | García-Archilla, Bosco
![]() ![]() ![]() ![]() ![]() ![]() ![]() Novo, Julia Titi, Edriss S. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2020 |
Deposit Date | 2023-12-19 |
Published in |
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Abstract | In this paper we analyze a finite element method applied to a continuous downscal-ing data assimilation algorithm for the numerical approximation of the two- and three-dimensionalNavier–Stokes equations corresponding to ... In this paper we analyze a finite element method applied to a continuous downscal-ing data assimilation algorithm for the numerical approximation of the two- and three-dimensionalNavier–Stokes equations corresponding to given measurements on a coarse spatial scale. For repre-senting the coarse mesh measurements we consider different types of interpolation operators includinga Lagrange interpolant. We obtain uniform-in-time estimates for the error between a finite elementapproximation and the reference solution corresponding to the coarse mesh measurements. We con-sider 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 inversepowers of the viscosity. Some numerical experiments illustrate the theoretical results. |
Funding agencies | Ministerio de Ciencia, Innovación y Universidades (MICINN). España Ministerio de Economía. España Junta de Castilla y León |
Project ID. | PGC2018096265-B-I00
![]() MTM2016-78995-P ![]() VA024P17 ![]() N00014-151-2333 ![]() |
Citation | García-Archilla, B., Novo, J. y Titi, E.S. (2020). Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations. SIAM Journal on Numerical Analysis, 58 (1), 410-429. https://doi.org/10.1137/19M1246845. |
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