Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation

An estimator for the error in the wave number is presented in the context of finite element approximations of the Helmholtz equation. The proposed estimate is an extension of the ideas introduced in Steffens and D'iez (Comput. Methods Appl. Mech. Engng 2009; 198:1389–1400). In the previous work...

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Autores: Steffens, Lindaura Maria, Parés Mariné, Núria|||0000-0002-2914-9904, Díez, Pedro|||0000-0001-6464-6407
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/117188
Acceso en línea:https://hdl.handle.net/2117/117188
https://dx.doi.org/10.1002/nme.3104
Access Level:acceso abierto
Palabra clave:Waves
Numerical analysis
wave problems
Helmholtz equation
a posteriori error estimation
error estimation of wave number
dispersion/pollution error
stabilized methods
Ones
Anàlisi numèrica
Classificació AMS::74 Mechanics of deformable solids::74J Waves
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
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repository_id_str
spelling Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equationSteffens, Lindaura MariaParés Mariné, Núria|||0000-0002-2914-9904Díez, Pedro|||0000-0001-6464-6407WavesNumerical analysiswave problemsHelmholtz equationa posteriori error estimationerror estimation of wave numberdispersion/pollution errorstabilized methodsOnesAnàlisi numèricaClassificació AMS::74 Mechanics of deformable solids::74J WavesClassificació AMS::65 Numerical analysis::65G Error analysis and interval analysisÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèricsÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciènciesAn estimator for the error in the wave number is presented in the context of finite element approximations of the Helmholtz equation. The proposed estimate is an extension of the ideas introduced in Steffens and D'iez (Comput. Methods Appl. Mech. Engng 2009; 198:1389–1400). In the previous work, the error assessment technique was developed for standard Galerkin approximations. Here, the methodology is extended to deal also with stabilized approximations of the Helmholtz equation. Thus, the accuracy of the stabilized solutions is analyzed, including also their sensitivity to the stabilization parameters depending on the mesh topology. The procedure builds up an inexpensive approximation of the exact solution, using post-processing techniques standard in error estimation analysis, from which the estimate of the error in the wave number is computed using a simple closed expression. The recovery technique used in Steffens and Díez (Comput. Methods Appl. Mech. Engng 2009; 198:1389–1400) is based in a polynomial least-squares fitting. Here a new recovery strategy is introduced, using exponential (in a complex setup, trigonometric) local approximations respecting the nature of the solution of the wave problem.Peer ReviewedJohn Wiley & sons20112011-06-1020182018-05-14journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/117188https://dx.doi.org/10.1002/nme.3104reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1171882026-05-27T15:37:01Z
dc.title.none.fl_str_mv Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
title Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
spellingShingle Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
Steffens, Lindaura Maria
Waves
Numerical analysis
wave problems
Helmholtz equation
a posteriori error estimation
error estimation of wave number
dispersion/pollution error
stabilized methods
Ones
Anàlisi numèrica
Classificació AMS::74 Mechanics of deformable solids::74J Waves
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
title_short Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
title_full Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
title_fullStr Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
title_full_unstemmed Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
title_sort Estimation of the dispersion error in the numerical wave number of standard and stabilized finite element approximations of the Helmholtz equation
dc.creator.none.fl_str_mv Steffens, Lindaura Maria
Parés Mariné, Núria|||0000-0002-2914-9904
Díez, Pedro|||0000-0001-6464-6407
author Steffens, Lindaura Maria
author_facet Steffens, Lindaura Maria
Parés Mariné, Núria|||0000-0002-2914-9904
Díez, Pedro|||0000-0001-6464-6407
author_role author
author2 Parés Mariné, Núria|||0000-0002-2914-9904
Díez, Pedro|||0000-0001-6464-6407
author2_role author
author
dc.subject.none.fl_str_mv Waves
Numerical analysis
wave problems
Helmholtz equation
a posteriori error estimation
error estimation of wave number
dispersion/pollution error
stabilized methods
Ones
Anàlisi numèrica
Classificació AMS::74 Mechanics of deformable solids::74J Waves
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
topic Waves
Numerical analysis
wave problems
Helmholtz equation
a posteriori error estimation
error estimation of wave number
dispersion/pollution error
stabilized methods
Ones
Anàlisi numèrica
Classificació AMS::74 Mechanics of deformable solids::74J Waves
Classificació AMS::65 Numerical analysis::65G Error analysis and interval analysis
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
description An estimator for the error in the wave number is presented in the context of finite element approximations of the Helmholtz equation. The proposed estimate is an extension of the ideas introduced in Steffens and D'iez (Comput. Methods Appl. Mech. Engng 2009; 198:1389–1400). In the previous work, the error assessment technique was developed for standard Galerkin approximations. Here, the methodology is extended to deal also with stabilized approximations of the Helmholtz equation. Thus, the accuracy of the stabilized solutions is analyzed, including also their sensitivity to the stabilization parameters depending on the mesh topology. The procedure builds up an inexpensive approximation of the exact solution, using post-processing techniques standard in error estimation analysis, from which the estimate of the error in the wave number is computed using a simple closed expression. The recovery technique used in Steffens and Díez (Comput. Methods Appl. Mech. Engng 2009; 198:1389–1400) is based in a polynomial least-squares fitting. Here a new recovery strategy is introduced, using exponential (in a complex setup, trigonometric) local approximations respecting the nature of the solution of the wave problem.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-06-10
2018
2018-05-14
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/117188
https://dx.doi.org/10.1002/nme.3104
url https://hdl.handle.net/2117/117188
https://dx.doi.org/10.1002/nme.3104
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv John Wiley & sons
publisher.none.fl_str_mv John Wiley & sons
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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