A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/44551 https://doi.org/10.1515/cmam-2013-0017 |
Resumo: | In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behavior is represented by a Voigt–Kelvin model or a Maxwell model. A finite difference discretization defined on a general non-uniform grid with second order convergence order in space is proposed. The analysis does not follow the usual splitting of the global error using the solution of an elliptic equation induced by the integro-differential equation. The new approach enables us to reduce the smoothness required to the theoretical solution when the usual split technique is used. Non-singular and singular kernels are considered. Numerical simulations which show the effectiveness of the method are included. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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A Second Order Approximation for Quasilinear Non-Fickian Diffusion ModelsIn this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behavior is represented by a Voigt–Kelvin model or a Maxwell model. A finite difference discretization defined on a general non-uniform grid with second order convergence order in space is proposed. The analysis does not follow the usual splitting of the global error using the solution of an elliptic equation induced by the integro-differential equation. The new approach enables us to reduce the smoothness required to the theoretical solution when the usual split technique is used. Non-singular and singular kernels are considered. Numerical simulations which show the effectiveness of the method are included.De Gruyter2013info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44551http://hdl.handle.net/10316/44551https://doi.org/10.1515/cmam-2013-0017https://doi.org/10.1515/cmam-2013-0017enghttps://doi.org/10.1515/cmam-2013-0017Ferreira, José AugustoGudin͂o, EliasOliveira, Paula deinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-09-03T11:28:50ZPortal AgregadorONG |
dc.title.none.fl_str_mv |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
title |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
spellingShingle |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models Ferreira, José Augusto |
title_short |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
title_full |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
title_fullStr |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
title_full_unstemmed |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
title_sort |
A Second Order Approximation for Quasilinear Non-Fickian Diffusion Models |
author |
Ferreira, José Augusto |
author_facet |
Ferreira, José Augusto Gudin͂o, Elias Oliveira, Paula de |
author_role |
author |
author2 |
Gudin͂o, Elias Oliveira, Paula de |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Ferreira, José Augusto Gudin͂o, Elias Oliveira, Paula de |
description |
In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behavior is represented by a Voigt–Kelvin model or a Maxwell model. A finite difference discretization defined on a general non-uniform grid with second order convergence order in space is proposed. The analysis does not follow the usual splitting of the global error using the solution of an elliptic equation induced by the integro-differential equation. The new approach enables us to reduce the smoothness required to the theoretical solution when the usual split technique is used. Non-singular and singular kernels are considered. Numerical simulations which show the effectiveness of the method are included. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/44551 http://hdl.handle.net/10316/44551 https://doi.org/10.1515/cmam-2013-0017 https://doi.org/10.1515/cmam-2013-0017 |
url |
http://hdl.handle.net/10316/44551 https://doi.org/10.1515/cmam-2013-0017 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1515/cmam-2013-0017 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
De Gruyter |
publisher.none.fl_str_mv |
De Gruyter |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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