An adaptive Wavelet-Galerkin method for parabolic partial differential equations

Autores
Vampa, Victoria Cristina; Martín, María Teresa
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.
En este trabajo se desarrolla un método Wavelet-Galerkin Adaptativo para la resolución de ecuaciones diferenciales parabólicas que modelan problemas físicos, con diferentes escalas en el espacio y en el tiempo. Se utiliza un esquema semi-implícito en diferencias temporales y la estructura multirresolución de las B-splines sobre intervalo. Como es sabido que en muchos casos las soluciones presentan gradientes localmente altos, se han diseñado estimadores locales de error y una estrategia adaptativa eficiente para elegir la escala apropiada en cada tiempo. Finalmente, se realizaron experimentos que ilustran la aplicabilidad y la eficiencia del método propuesto.
Facultad de Ciencias Exactas
Facultad de Ingeniería
Materia
Ciencias Exactas
Ingeniería
Matemática
B-spline
Multiresolution analysis
Wavelet-Galerkin
Adaptive
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/100002

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oai_identifier_str oai:sedici.unlp.edu.ar:10915/100002
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling An adaptive Wavelet-Galerkin method for parabolic partial differential equationsUn método Wavelet-Galerkin adaptativo para ecuaciones diferenciales parciales parabólicasVampa, Victoria CristinaMartín, María TeresaCiencias ExactasIngenieríaMatemáticaB-splineMultiresolution analysisWavelet-GalerkinAdaptiveIn this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.En este trabajo se desarrolla un método Wavelet-Galerkin Adaptativo para la resolución de ecuaciones diferenciales parabólicas que modelan problemas físicos, con diferentes escalas en el espacio y en el tiempo. Se utiliza un esquema semi-implícito en diferencias temporales y la estructura multirresolución de las B-splines sobre intervalo. Como es sabido que en muchos casos las soluciones presentan gradientes localmente altos, se han diseñado estimadores locales de error y una estrategia adaptativa eficiente para elegir la escala apropiada en cada tiempo. Finalmente, se realizaron experimentos que ilustran la aplicabilidad y la eficiencia del método propuesto.Facultad de Ciencias ExactasFacultad de Ingeniería2015-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf71-87http://sedici.unlp.edu.ar/handle/10915/100002enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/51519info:eu-repo/semantics/altIdentifier/issn/2215-3373info:eu-repo/semantics/altIdentifier/hdl/11336/51519info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:20:06Zoai:sedici.unlp.edu.ar:10915/100002Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:20:06.995SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv An adaptive Wavelet-Galerkin method for parabolic partial differential equations
Un método Wavelet-Galerkin adaptativo para ecuaciones diferenciales parciales parabólicas
title An adaptive Wavelet-Galerkin method for parabolic partial differential equations
spellingShingle An adaptive Wavelet-Galerkin method for parabolic partial differential equations
Vampa, Victoria Cristina
Ciencias Exactas
Ingeniería
Matemática
B-spline
Multiresolution analysis
Wavelet-Galerkin
Adaptive
title_short An adaptive Wavelet-Galerkin method for parabolic partial differential equations
title_full An adaptive Wavelet-Galerkin method for parabolic partial differential equations
title_fullStr An adaptive Wavelet-Galerkin method for parabolic partial differential equations
title_full_unstemmed An adaptive Wavelet-Galerkin method for parabolic partial differential equations
title_sort An adaptive Wavelet-Galerkin method for parabolic partial differential equations
dc.creator.none.fl_str_mv Vampa, Victoria Cristina
Martín, María Teresa
author Vampa, Victoria Cristina
author_facet Vampa, Victoria Cristina
Martín, María Teresa
author_role author
author2 Martín, María Teresa
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Ingeniería
Matemática
B-spline
Multiresolution analysis
Wavelet-Galerkin
Adaptive
topic Ciencias Exactas
Ingeniería
Matemática
B-spline
Multiresolution analysis
Wavelet-Galerkin
Adaptive
dc.description.none.fl_txt_mv In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.
En este trabajo se desarrolla un método Wavelet-Galerkin Adaptativo para la resolución de ecuaciones diferenciales parabólicas que modelan problemas físicos, con diferentes escalas en el espacio y en el tiempo. Se utiliza un esquema semi-implícito en diferencias temporales y la estructura multirresolución de las B-splines sobre intervalo. Como es sabido que en muchos casos las soluciones presentan gradientes localmente altos, se han diseñado estimadores locales de error y una estrategia adaptativa eficiente para elegir la escala apropiada en cada tiempo. Finalmente, se realizaron experimentos que ilustran la aplicabilidad y la eficiencia del método propuesto.
Facultad de Ciencias Exactas
Facultad de Ingeniería
description In this paper an Adaptive Wavelet-Galerkin method for the solution of parabolic partial differential equations modeling physical problems with different spatial and temporal scales is developed. A semi-implicit time difference scheme is applied and B-spline multiresolution structure on the interval is used. As in many cases these solutions are known to present localized sharp gradients, local error estimators are designed and an efficient adaptive strategy to choose the appropriate scale for each time is developed. Finally, experiments were performed to illustrate the applicability and efficiency of the proposed method.
publishDate 2015
dc.date.none.fl_str_mv 2015-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/100002
url http://sedici.unlp.edu.ar/handle/10915/100002
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/51519
info:eu-repo/semantics/altIdentifier/issn/2215-3373
info:eu-repo/semantics/altIdentifier/hdl/11336/51519
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
71-87
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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