Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps

© The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Detalles Bibliográficos
Autores: García-Archilla, Bosco, Novo, Julia
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/152944
Acceso en línea:https://hdl.handle.net/11441/152944
https://doi.org/10.1093/imanum/drac058
Access Level:acceso abierto
Palabra clave:Incompressible Navier–Stokes equations
Variable step BDF2
Implicit–explicit methods
Graddiv stabilization
Robust error bounds
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spelling Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable stepsGarcía-Archilla, BoscoNovo, JuliaIncompressible Navier–Stokes equationsVariable step BDF2Implicit–explicit methodsGraddiv stabilizationRobust error bounds© The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.This paper studies fully discrete finite element approximations to the Navier–Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration, two implicit–explicit second-order backward differentiation formulae (BDF2) schemes are applied. In both, the Laplacian is implicit while the nonlinear term is explicit, in the first one, and semiimplicit, in the second one. The grad-div stabilization allows us to prove error bounds in which the constants are independent of inverse powers of the viscosity. Error bounds of order in space are obtained for the error of the velocity using piecewise polynomials of degree to approximate the velocity together with second-order bounds in time, both for fixed time-step methods and for methods with variable time steps. A Courant Friedrichs Lewy (CFL)-type condition is needed for the method in which the nonlinear term is explicit relating time-step and spatial mesh-size parameters.Ministerio de Ciencia, Innovación y Universidades PGC2018-096265-B-I00 - PID2019-104141GB-I00Ministerio de Economía PID2019-104141GB-I00 - VA169P20Oxford University Press / Institute of Mathematics and its ApplicationsMatemática Aplicada IITIC130: Investigación en Sistemas Dinámicos en IngenieríaMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaMinisterio de Economía. España2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/152944https://doi.org/10.1093/imanum/drac058reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésIMA Journal of Numerical Analysis, 43 (5), 2892-2933.PGC2018-096265-B-I00PID2019-104141GB-I00VA169P20https://academic.oup.com/imajna/article/43/5/2892/6748175info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1529442026-06-17T12:51:07Z
dc.title.none.fl_str_mv Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
title Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
spellingShingle Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
García-Archilla, Bosco
Incompressible Navier–Stokes equations
Variable step BDF2
Implicit–explicit methods
Graddiv stabilization
Robust error bounds
title_short Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
title_full Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
title_fullStr Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
title_full_unstemmed Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
title_sort Robust error bounds for the Navier-Stokes equations using implicit-explicit second-order BDF method with variable steps
dc.creator.none.fl_str_mv García-Archilla, Bosco
Novo, Julia
author García-Archilla, Bosco
author_facet García-Archilla, Bosco
Novo, Julia
author_role author
author2 Novo, Julia
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada II
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Ministerio de Economía. España
dc.subject.none.fl_str_mv Incompressible Navier–Stokes equations
Variable step BDF2
Implicit–explicit methods
Graddiv stabilization
Robust error bounds
topic Incompressible Navier–Stokes equations
Variable step BDF2
Implicit–explicit methods
Graddiv stabilization
Robust error bounds
description © The Author(s) 2022. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/152944
https://doi.org/10.1093/imanum/drac058
url https://hdl.handle.net/11441/152944
https://doi.org/10.1093/imanum/drac058
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv IMA Journal of Numerical Analysis, 43 (5), 2892-2933.
PGC2018-096265-B-I00
PID2019-104141GB-I00
VA169P20
https://academic.oup.com/imajna/article/43/5/2892/6748175
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press / Institute of Mathematics and its Applications
publisher.none.fl_str_mv Oxford University Press / Institute of Mathematics and its Applications
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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