Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations

First Published in SIAM Journal on Numerical Analysis in 2020, Vol. 58, No. 1, published by the Society for Industrial and Applied Mathematics (SIAM)

Detalles Bibliográficos
Autores: García-Archilla, Bosco, Novo Martín, Julia, Titi, Edriss S.
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/689924
Acceso en línea:http://hdl.handle.net/10486/689924
https://dx.doi.org/10.1137/19M1246845
Access Level:acceso abierto
Palabra clave:Data assimilation
Downscaling
Navier-Stokes equations
Uniform-in-time error estimates
Mixed nite elements
Matemáticas
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spelling Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes EquationsGarcía-Archilla, BoscoNovo Martín, JuliaTiti, Edriss S.Data assimilationDownscalingNavier-Stokes equationsUniform-in-time error estimatesMixed nite elementsMatemáticasFirst Published in SIAM Journal on Numerical Analysis in 2020, Vol. 58, No. 1, published by the Society for Industrial and Applied Mathematics (SIAM)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 resultsDepartamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain. Research is supported by Spanish MINECO under grant MTM2015-65608-P (bosco@esi.us.es). Departamento de Matemáticas, Universidad Autónoma de Madrid, Spain. Research is supported by Spanish MINECO under grant MTM2016-78995-P (AEI/FEDER, UE) and VA024P17 (Junta de Castilla y Leon, ES) co nanced by FEDER funds (julia.novo@uam.es). Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. De- partment of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel. Research is supported in part by the ONR grant N00014-15-1-2333, the Einstein Stiftung/Foundation - Berlin, through the Einstein Visiting Fellow Program, and by the John Simon Guggenheim Memorial Foundation (titi@math.tamu.edu, Edriss.Titi@damtp.cam.ac.uk).Society for Industrial and Applied MathematicsDepartamento de MatemáticasFacultad de Ciencias20202020-01-21research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/689924https://dx.doi.org/10.1137/19M1246845reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/6899242026-06-23T12:46:27Z
dc.title.none.fl_str_mv Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
title Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
spellingShingle Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
García-Archilla, Bosco
Data assimilation
Downscaling
Navier-Stokes equations
Uniform-in-time error estimates
Mixed nite elements
Matemáticas
title_short Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
title_full Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
title_fullStr Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
title_full_unstemmed Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
title_sort Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier Stokes Equations
dc.creator.none.fl_str_mv García-Archilla, Bosco
Novo Martín, Julia
Titi, Edriss S.
author García-Archilla, Bosco
author_facet García-Archilla, Bosco
Novo Martín, Julia
Titi, Edriss S.
author_role author
author2 Novo Martín, Julia
Titi, Edriss S.
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Data assimilation
Downscaling
Navier-Stokes equations
Uniform-in-time error estimates
Mixed nite elements
Matemáticas
topic Data assimilation
Downscaling
Navier-Stokes equations
Uniform-in-time error estimates
Mixed nite elements
Matemáticas
description First Published in SIAM Journal on Numerical Analysis in 2020, Vol. 58, No. 1, published by the Society for Industrial and Applied Mathematics (SIAM)
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-21
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/689924
https://dx.doi.org/10.1137/19M1246845
url http://hdl.handle.net/10486/689924
https://dx.doi.org/10.1137/19M1246845
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
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