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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/100002
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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 |
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