ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Interdisciplinar de Pesquisa em Engenharia |
Texto Completo: | https://periodicos.unb.br/index.php/ripe/article/view/21365 |
Resumo: | This investigation proposes the use of continuous strong”“form residuum fields, obtained through smooth Generalized Finite Element Method (GFEM) , for error estimation in terms of the energy norm. Aspects on the construction of Ck”“GFEM”“based approximation functions (Duarte, Kim & Quaresma, 2006), using domain triangulation, are addressed. It is shown how the smoothness may be exploited in implicit residual algorithms for error estimation since the approximated Ck”“GFEM stress field can be directly continuously differentiated, to verify the equilibrium equations in strong form, locally, and then leading to a continuous residuum field. The subdomain strategy (Barros et al., 2013; Par´es, D´Ä±ez & Huerta, 2006) for implicit error estimation is employed, in such a way the local error problems are defined on the clouds, the patch of elements around the node, through the weighting provided by the Partition of Unity (PoU) functions. Its implementation fits very well into GFEM routines because such strategy is naturally tailored to the nodal enrichment procedure of the method (Barros, Barcellos & Duarte, 2007), producing nodal error indicators. Two types of weighting for the variational residuum functional (Prudhomme et al., 2004; Strouboulis et al., 2006) are tested in order to verify the performance for the effectivity of the nodal indicators and the global estimators. Numerical examples show that both the indicator and the estimator may be effective for two-dimensional linear elastic problems even in the presence of singularities. |
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ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONSSubdomain error estimators. Implicit residual methods. Ck”“GFEM. Smoothness. Strong-form residuum field.This investigation proposes the use of continuous strong”“form residuum fields, obtained through smooth Generalized Finite Element Method (GFEM) , for error estimation in terms of the energy norm. Aspects on the construction of Ck”“GFEM”“based approximation functions (Duarte, Kim & Quaresma, 2006), using domain triangulation, are addressed. It is shown how the smoothness may be exploited in implicit residual algorithms for error estimation since the approximated Ck”“GFEM stress field can be directly continuously differentiated, to verify the equilibrium equations in strong form, locally, and then leading to a continuous residuum field. The subdomain strategy (Barros et al., 2013; Par´es, D´Ä±ez & Huerta, 2006) for implicit error estimation is employed, in such a way the local error problems are defined on the clouds, the patch of elements around the node, through the weighting provided by the Partition of Unity (PoU) functions. Its implementation fits very well into GFEM routines because such strategy is naturally tailored to the nodal enrichment procedure of the method (Barros, Barcellos & Duarte, 2007), producing nodal error indicators. Two types of weighting for the variational residuum functional (Prudhomme et al., 2004; Strouboulis et al., 2006) are tested in order to verify the performance for the effectivity of the nodal indicators and the global estimators. Numerical examples show that both the indicator and the estimator may be effective for two-dimensional linear elastic problems even in the presence of singularities.Programa de Pós-Graduação em Integridade de Materiais da Engenharia2017-01-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.unb.br/index.php/ripe/article/view/2136510.26512/ripe.v2i14.21365Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 114-133Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 114-1332447-6102reponame:Revista Interdisciplinar de Pesquisa em Engenhariainstname:Universidade de Brasília (UnB)instacron:UNBenghttps://periodicos.unb.br/index.php/ripe/article/view/21365/19708Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPEinfo:eu-repo/semantics/openAccessTorres, Diego Amadeu F.Barcellos, Clovis Sperb deBarros, Felício Bruzzi2019-06-16T02:28:06Zoai:ojs.pkp.sfu.ca:article/21365Revistahttps://periodicos.unb.br/index.php/ripePUBhttps://periodicos.unb.br/index.php/ripe/oaianflor@unb.br2447-61022447-6102opendoar:2019-06-16T02:28:06Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB)false |
dc.title.none.fl_str_mv |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
title |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
spellingShingle |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS Torres, Diego Amadeu F. Subdomain error estimators. Implicit residual methods. Ck”“GFEM. Smoothness. Strong-form residuum field. |
title_short |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
title_full |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
title_fullStr |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
title_full_unstemmed |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
title_sort |
ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS |
author |
Torres, Diego Amadeu F. |
author_facet |
Torres, Diego Amadeu F. Barcellos, Clovis Sperb de Barros, Felício Bruzzi |
author_role |
author |
author2 |
Barcellos, Clovis Sperb de Barros, Felício Bruzzi |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Torres, Diego Amadeu F. Barcellos, Clovis Sperb de Barros, Felício Bruzzi |
dc.subject.por.fl_str_mv |
Subdomain error estimators. Implicit residual methods. Ck”“GFEM. Smoothness. Strong-form residuum field. |
topic |
Subdomain error estimators. Implicit residual methods. Ck”“GFEM. Smoothness. Strong-form residuum field. |
description |
This investigation proposes the use of continuous strong”“form residuum fields, obtained through smooth Generalized Finite Element Method (GFEM) , for error estimation in terms of the energy norm. Aspects on the construction of Ck”“GFEM”“based approximation functions (Duarte, Kim & Quaresma, 2006), using domain triangulation, are addressed. It is shown how the smoothness may be exploited in implicit residual algorithms for error estimation since the approximated Ck”“GFEM stress field can be directly continuously differentiated, to verify the equilibrium equations in strong form, locally, and then leading to a continuous residuum field. The subdomain strategy (Barros et al., 2013; Par´es, D´Ä±ez & Huerta, 2006) for implicit error estimation is employed, in such a way the local error problems are defined on the clouds, the patch of elements around the node, through the weighting provided by the Partition of Unity (PoU) functions. Its implementation fits very well into GFEM routines because such strategy is naturally tailored to the nodal enrichment procedure of the method (Barros, Barcellos & Duarte, 2007), producing nodal error indicators. Two types of weighting for the variational residuum functional (Prudhomme et al., 2004; Strouboulis et al., 2006) are tested in order to verify the performance for the effectivity of the nodal indicators and the global estimators. Numerical examples show that both the indicator and the estimator may be effective for two-dimensional linear elastic problems even in the presence of singularities. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-30 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21365 10.26512/ripe.v2i14.21365 |
url |
https://periodicos.unb.br/index.php/ripe/article/view/21365 |
identifier_str_mv |
10.26512/ripe.v2i14.21365 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21365/19708 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
dc.source.none.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 114-133 Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 14 (2016): DEVELOPMENTS AND APPLICATIONS OF SPECIAL ENRICHMENT METHODS AND INNOVATE DISCRETIZATION TECHNIQUES; 114-133 2447-6102 reponame:Revista Interdisciplinar de Pesquisa em Engenharia instname:Universidade de Brasília (UnB) instacron:UNB |
instname_str |
Universidade de Brasília (UnB) |
instacron_str |
UNB |
institution |
UNB |
reponame_str |
Revista Interdisciplinar de Pesquisa em Engenharia |
collection |
Revista Interdisciplinar de Pesquisa em Engenharia |
repository.name.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB) |
repository.mail.fl_str_mv |
anflor@unb.br |
_version_ |
1798315226114818048 |