Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality

Autores
Olguin, Mariela Carina; Tarzia, Domingo Alberto
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The objective of this work is to make the numerical analysis, through the finite element method with Lagrange's triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.
Fil: Olguin, Mariela Carina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; Argentina
Materia
Optimal control
Numerical analysis
Elliptic variational inequalities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/52974
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/52974
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network_name_str CONICET Digital (CONICET)
spelling Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational InequalityOlguin, Mariela CarinaTarzia, Domingo AlbertoOptimal controlNumerical analysisElliptic variational inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The objective of this work is to make the numerical analysis, through the finite element method with Lagrange's triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.Fil: Olguin, Mariela Carina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; ArgentinaFil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; ArgentinaHindawi Publishing Corporation2015-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/52974Olguin, Mariela Carina; Tarzia, Domingo Alberto; Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality; Hindawi Publishing Corporation; International Journal of Differential Equations; 2015; 9-2015; 1-71687-9651CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1155/2015/407930info:eu-repo/semantics/altIdentifier/url/https://www.hindawi.com/journals/ijde/2015/407930/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:25:03Zoai:ri.conicet.gov.ar:11336/52974instacron: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:34982025-10-15 14:25:04.105CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
title Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
spellingShingle Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
Olguin, Mariela Carina
Optimal control
Numerical analysis
Elliptic variational inequalities
title_short Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
title_full Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
title_fullStr Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
title_full_unstemmed Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
title_sort Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality
dc.creator.none.fl_str_mv Olguin, Mariela Carina
Tarzia, Domingo Alberto
author Olguin, Mariela Carina
author_facet Olguin, Mariela Carina
Tarzia, Domingo Alberto
author_role author
author2 Tarzia, Domingo Alberto
author2_role author
dc.subject.none.fl_str_mv Optimal control
Numerical analysis
Elliptic variational inequalities
topic Optimal control
Numerical analysis
Elliptic variational inequalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The objective of this work is to make the numerical analysis, through the finite element method with Lagrange's triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.
Fil: Olguin, Mariela Carina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Austral; Argentina
description The objective of this work is to make the numerical analysis, through the finite element method with Lagrange's triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energy g. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positive h (the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameter h goes to zero.
publishDate 2015
dc.date.none.fl_str_mv 2015-09
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/11336/52974
Olguin, Mariela Carina; Tarzia, Domingo Alberto; Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality; Hindawi Publishing Corporation; International Journal of Differential Equations; 2015; 9-2015; 1-7
1687-9651
CONICET Digital
CONICET
url http://hdl.handle.net/11336/52974
identifier_str_mv Olguin, Mariela Carina; Tarzia, Domingo Alberto; Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality; Hindawi Publishing Corporation; International Journal of Differential Equations; 2015; 9-2015; 1-7
1687-9651
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1155/2015/407930
info:eu-repo/semantics/altIdentifier/url/https://www.hindawi.com/journals/ijde/2015/407930/
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 Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
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
_version_ 1846082680164188160
score 13.22299

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