Pointwise error bounds in POD methods without difference quotients

In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots....

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Detalles Bibliográficos
Autores: García-Archilla, Bosco, Novo Martín, Julia
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/171997
Acceso en línea:https://hdl.handle.net/11441/171997
https://doi.org/10.1007/s10915-025-02838-9
Access Level:acceso abierto
Palabra clave:Proper orthogonal decomposition
Error analysis
Pointwise error estimates in time
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spelling Pointwise error bounds in POD methods without difference quotientsGarcía-Archilla, BoscoNovo Martín, JuliaProper orthogonal decompositionError analysisPointwise error estimates in timeIn this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots. More recently, the inclusion of DQs has allowed to obtain pointwise (as opposed to averaged) error bounds that decay with the same convergence rate (in terms of the POD singular values) as averaged ones. In the present paper, for POD methods not including DQs in their data set, we obtain error bounds that do not degrade with the number of snapshots if the function from where the snapshots are taken has certain degree of smoothness. Moreover, the rate of convergence is as close as that of methods including DQs as the smoothness of the function providing the snapshots allows. We do this by obtaining discrete counterparts of Agmon and interpolation inequalities in Sobolev spaces. Numerical experiments validating these estimates are also presented.SpringerMatemática Aplicada IITIC130: Investigación en Sistemas Dinámicos en IngenieríaMinisterio de Ciencia e Innovación (MICIN). EspañaEuropean Union (UE)2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/171997https://doi.org/10.1007/s10915-025-02838-9reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Scientific Computing, 103, 24.PID2021-123200NB-I00PID2022-136550NB-I00https://link.springer.com/article/10.1007/s10915-025-02838-9info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1719972026-06-17T12:51:07Z
dc.title.none.fl_str_mv Pointwise error bounds in POD methods without difference quotients
title Pointwise error bounds in POD methods without difference quotients
spellingShingle Pointwise error bounds in POD methods without difference quotients
García-Archilla, Bosco
Proper orthogonal decomposition
Error analysis
Pointwise error estimates in time
title_short Pointwise error bounds in POD methods without difference quotients
title_full Pointwise error bounds in POD methods without difference quotients
title_fullStr Pointwise error bounds in POD methods without difference quotients
title_full_unstemmed Pointwise error bounds in POD methods without difference quotients
title_sort Pointwise error bounds in POD methods without difference quotients
dc.creator.none.fl_str_mv García-Archilla, Bosco
Novo Martín, Julia
author García-Archilla, Bosco
author_facet García-Archilla, Bosco
Novo Martín, Julia
author_role author
author2 Novo Martín, Julia
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada II
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Ministerio de Ciencia e Innovación (MICIN). España
European Union (UE)
dc.subject.none.fl_str_mv Proper orthogonal decomposition
Error analysis
Pointwise error estimates in time
topic Proper orthogonal decomposition
Error analysis
Pointwise error estimates in time
description In this paper we consider proper orthogonal decomposition (POD) methods that do not include difference quotients (DQs) of snapshots in the data set. The inclusion of DQs have been shown in the literature to be a key element in obtaining error bounds that do not degrade with the number of snapshots. More recently, the inclusion of DQs has allowed to obtain pointwise (as opposed to averaged) error bounds that decay with the same convergence rate (in terms of the POD singular values) as averaged ones. In the present paper, for POD methods not including DQs in their data set, we obtain error bounds that do not degrade with the number of snapshots if the function from where the snapshots are taken has certain degree of smoothness. Moreover, the rate of convergence is as close as that of methods including DQs as the smoothness of the function providing the snapshots allows. We do this by obtaining discrete counterparts of Agmon and interpolation inequalities in Sobolev spaces. Numerical experiments validating these estimates are also presented.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/171997
https://doi.org/10.1007/s10915-025-02838-9
url https://hdl.handle.net/11441/171997
https://doi.org/10.1007/s10915-025-02838-9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Scientific Computing, 103, 24.
PID2021-123200NB-I00
PID2022-136550NB-I00
https://link.springer.com/article/10.1007/s10915-025-02838-9
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 Springer
publisher.none.fl_str_mv Springer
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
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