An adaptive wavelet-galerkin method for parabolic partial differentia equations
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...
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Universidad de Costa Rica
2015-01-01
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Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/17556 |
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doaj-cec5e3e253b440d29228c62ffd463e7a2020-11-24T21:59:10ZspaUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732015-01-01221718710.15517/rmta.v22i1.1755616183An adaptive wavelet-galerkin method for parabolic partial differentia equationsVictoria Vampa0María T. Martín1Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata, ArgentinaFacultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina. IFLP-CCT- CONICET, C. C. 727, 1900 La Plata, Argentina.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.https://revistas.ucr.ac.cr/index.php/matematica/article/view/17556B-splinemultiresolution analysiswavelet-Galerkin |
collection |
DOAJ |
language |
Spanish |
format |
Article |
sources |
DOAJ |
author |
Victoria Vampa María T. Martín |
spellingShingle |
Victoria Vampa María T. Martín An adaptive wavelet-galerkin method for parabolic partial differentia equations Revista de Matemática: Teoría y Aplicaciones B-spline multiresolution analysis wavelet-Galerkin |
author_facet |
Victoria Vampa María T. Martín |
author_sort |
Victoria Vampa |
title |
An adaptive wavelet-galerkin method for parabolic partial differentia equations |
title_short |
An adaptive wavelet-galerkin method for parabolic partial differentia equations |
title_full |
An adaptive wavelet-galerkin method for parabolic partial differentia equations |
title_fullStr |
An adaptive wavelet-galerkin method for parabolic partial differentia equations |
title_full_unstemmed |
An adaptive wavelet-galerkin method for parabolic partial differentia equations |
title_sort |
adaptive wavelet-galerkin method for parabolic partial differentia equations |
publisher |
Universidad de Costa Rica |
series |
Revista de Matemática: Teoría y Aplicaciones |
issn |
2215-3373 |
publishDate |
2015-01-01 |
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. |
topic |
B-spline multiresolution analysis wavelet-Galerkin |
url |
https://revistas.ucr.ac.cr/index.php/matematica/article/view/17556 |
work_keys_str_mv |
AT victoriavampa anadaptivewaveletgalerkinmethodforparabolicpartialdifferentiaequations AT mariatmartin anadaptivewaveletgalerkinmethodforparabolicpartialdifferentiaequations AT victoriavampa adaptivewaveletgalerkinmethodforparabolicpartialdifferentiaequations AT mariatmartin adaptivewaveletgalerkinmethodforparabolicpartialdifferentiaequations |
_version_ |
1725848697667846144 |