The Steklov eigenvalue problem in a cuspidal domain

In this paper we analyze the approximation, by piecewise linear finite elements, of a Steklov eigenvalue problem in a plane domain with an external cusp. This problem is not covered by the literature and its analysis requires a special treatment. Indeed, we develop new trace theorems and we also obt...

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Detalles Bibliográficos
Autores: Armentano, Maria Gabriela, Lombardi, Ariel Luis
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/143897
Acceso en línea:http://hdl.handle.net/11336/143897
Access Level:acceso abierto
Palabra clave:Steklov eigenvalue problem
finite elements
cuspidal domains
graded meshes
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling The Steklov eigenvalue problem in a cuspidal domainArmentano, Maria GabrielaLombardi, Ariel LuisSteklov eigenvalue problemfinite elementscuspidal domainsgraded mesheshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we analyze the approximation, by piecewise linear finite elements, of a Steklov eigenvalue problem in a plane domain with an external cusp. This problem is not covered by the literature and its analysis requires a special treatment. Indeed, we develop new trace theorems and we also obtain regularity results for the source counterpart. Moreover, under appropriate assumptions on the meshes, we present interpolation error estimates for functions in fractional Sobolev spaces. These estimates allow us to obtain appropriate convergence results of the source counterpart which, in the context of the theory of compact operator, are a fundamental tool in order to prove the convergence of the eigenpairs. At the end, we prove the convergence of the eigenpairs by using graded meshes and present some numerical tests.Fil: Armentano, Maria Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Lombardi, Ariel Luis. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaSpringer2020-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143897Armentano, Maria Gabriela; Lombardi, Ariel Luis; The Steklov eigenvalue problem in a cuspidal domain; Springer; Numerische Mathematik; 144; 2; 2-2020; 237-2700029-599XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00211-019-01092-0info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00211-019-01092-0info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T14:01:19Zoai:ri.conicet.gov.ar:11336/143897instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982024-05-08 14:01:19.914CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Steklov eigenvalue problem in a cuspidal domain
title The Steklov eigenvalue problem in a cuspidal domain
spellingShingle The Steklov eigenvalue problem in a cuspidal domain
Armentano, Maria Gabriela
Steklov eigenvalue problem
finite elements
cuspidal domains
graded meshes
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short The Steklov eigenvalue problem in a cuspidal domain
title_full The Steklov eigenvalue problem in a cuspidal domain
title_fullStr The Steklov eigenvalue problem in a cuspidal domain
title_full_unstemmed The Steklov eigenvalue problem in a cuspidal domain
title_sort The Steklov eigenvalue problem in a cuspidal domain
dc.creator.none.fl_str_mv Armentano, Maria Gabriela
Lombardi, Ariel Luis
author Armentano, Maria Gabriela
author_facet Armentano, Maria Gabriela
Lombardi, Ariel Luis
author_role author
author2 Lombardi, Ariel Luis
author2_role author
dc.subject.none.fl_str_mv Steklov eigenvalue problem
finite elements
cuspidal domains
graded meshes
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic Steklov eigenvalue problem
finite elements
cuspidal domains
graded meshes
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper we analyze the approximation, by piecewise linear finite elements, of a Steklov eigenvalue problem in a plane domain with an external cusp. This problem is not covered by the literature and its analysis requires a special treatment. Indeed, we develop new trace theorems and we also obtain regularity results for the source counterpart. Moreover, under appropriate assumptions on the meshes, we present interpolation error estimates for functions in fractional Sobolev spaces. These estimates allow us to obtain appropriate convergence results of the source counterpart which, in the context of the theory of compact operator, are a fundamental tool in order to prove the convergence of the eigenpairs. At the end, we prove the convergence of the eigenpairs by using graded meshes and present some numerical tests.
publishDate 2020
dc.date.none.fl_str_mv 2020-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/143897
Armentano, Maria Gabriela; Lombardi, Ariel Luis; The Steklov eigenvalue problem in a cuspidal domain; Springer; Numerische Mathematik; 144; 2; 2-2020; 237-270
0029-599X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143897
identifier_str_mv Armentano, Maria Gabriela; Lombardi, Ariel Luis; The Steklov eigenvalue problem in a cuspidal domain; Springer; Numerische Mathematik; 144; 2; 2-2020; 237-270
0029-599X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00211-019-01092-0
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00211-019-01092-0
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 15,81155

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