Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization

This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Frutos, J. de, García-Archilla, B., John, V., & Novo, J. (2019). Error analysis of non inf-sup stable discretizations of the time...

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Detalles Bibliográficos
Autores: de Frutos, Javier, García-Archilla, Bosco, John, Volker, Novo Martín, Julia
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/689936
Acceso en línea:http://hdl.handle.net/10486/689936
https://dx.doi.org/10.1093/imanum/dry044
Access Level:acceso abierto
Palabra clave:Navier-Stokes equations
Non inf-sup stable mixed finite elements
Local projection stabilization
Matemáticas
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spelling Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilizationde Frutos, JavierGarcía-Archilla, BoscoJohn, VolkerNovo Martín, JuliaNavier-Stokes equationsNon inf-sup stable mixed finite elementsLocal projection stabilizationMatemáticasThis is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Frutos, J. de, García-Archilla, B., John, V., & Novo, J. (2019). Error analysis of non inf-sup stable discretizations of the time-dependent Navier–Stokes equations with local projection stabilization. IMA Journal of Numerical Analysis, 39(4), 1747-1786 is available online at https://academic.oup.com/imajna/article-abstract/39/4/1747/5055331This paper studies non inf-sup stable finite element approximations to the evolutionary Navier-Stokes equations. Several local projection stabilization (LPS) methods corresponding to different stabilization terms are analyzed, thereby separately studying the effects of the different stabilization terms. Error estimates are derived in which the constants are independent of inverse powers of the viscosity. For one of the methods, using velocity and pressure finite elements of degree $l$, it will be proved that the velocity error in $L^\infty (0,T;L^2(\varOmega)) $ decays with rate $l+1/2$ in the case that $\nu \le h$, with $\nu$ being the dimensionless viscosity and $h$ being the mesh width. In the analysis of another method it was observed that the convective term can be bounded in an optimal way with the LPS stabilization of the pressure gradient. Numerical studies confirm the analytical resultsInstituto de Investigación en Matemáticas (IMUVA), Universidad de Valladolid, Spain. Research supported by Spanish MINECO under grants MTM2013-42538-P (MINECO, ES) and MTM2016-78995-P (AEI/FEDER, UE) and VA024P17 (Junta de Castilla y Leon, ES) cofinanced by FEDER funds. (frutos@mac.uva.es) Departamento de Matemática Aplicada II, Universidad de Sevilla, Sevilla, Spain. Research supported by Spanish MINECO under grant MTM2015-65608-P (bosco@esi.us.es) Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e. V. (WIAS), Mohrenstr. 39, 10117 Berlin, Germany. Freie Universit at Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany. Departamento de Matemáticas, Universidad Autónoma de Madrid, Spain. Research supported by Spanish MINECO under grants MTM2013-42538-P (MINECO, ES) and MTM2016-78995-P (AEI/FEDER, UE) and VA024P17 (Junta de Castilla y Leon, ES) cofinanced by FEDER funds (julia.novo@uam.es)Oxford University PressDepartamento de MatemáticasFacultad de Ciencias20182018-07-18research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/689936https://dx.doi.org/10.1093/imanum/dry044reponame: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:10486/6899362026-06-23T12:46:27Z
dc.title.none.fl_str_mv Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
title Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
spellingShingle Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
de Frutos, Javier
Navier-Stokes equations
Non inf-sup stable mixed finite elements
Local projection stabilization
Matemáticas
title_short Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
title_full Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
title_fullStr Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
title_full_unstemmed Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
title_sort Error analysis of non inf-sup stable discretizations of the time-dependent Navier-Stokes equations with local projection stabilization
dc.creator.none.fl_str_mv de Frutos, Javier
García-Archilla, Bosco
John, Volker
Novo Martín, Julia
author de Frutos, Javier
author_facet de Frutos, Javier
García-Archilla, Bosco
John, Volker
Novo Martín, Julia
author_role author
author2 García-Archilla, Bosco
John, Volker
Novo Martín, Julia
author2_role author
author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Navier-Stokes equations
Non inf-sup stable mixed finite elements
Local projection stabilization
Matemáticas
topic Navier-Stokes equations
Non inf-sup stable mixed finite elements
Local projection stabilization
Matemáticas
description This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Frutos, J. de, García-Archilla, B., John, V., & Novo, J. (2019). Error analysis of non inf-sup stable discretizations of the time-dependent Navier–Stokes equations with local projection stabilization. IMA Journal of Numerical Analysis, 39(4), 1747-1786 is available online at https://academic.oup.com/imajna/article-abstract/39/4/1747/5055331
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-07-18
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/10486/689936
https://dx.doi.org/10.1093/imanum/dry044
url http://hdl.handle.net/10486/689936
https://dx.doi.org/10.1093/imanum/dry044
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 Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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