A posteriori error analysis for optimization with PDE constraints

Autores
Gaspoz, Fernando Daniel; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.
Fil: Gaspoz, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Kreuzer, Christian. Universität Dortmund; Alemania
Fil: Veeser, Andreas. Università degli Studi di Milano; Italia
Fil: Wollner, Winnifried. Universitat Hamburg; Alemania
Materia
CONTROL
FINITE ELEMENTS
ADAPTIVITY
OPTIMIZATION
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:11336/272429
Acceder
id CONICETDig_4277a573daa601a3c6cc0ed8f1e55a28
oai_identifier_str oai:ri.conicet.gov.ar:11336/272429
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A posteriori error analysis for optimization with PDE constraintsGaspoz, Fernando DanielKreuzer, ChristianVeeser, AndreasWollner, WinnifriedCONTROLFINITE ELEMENTSADAPTIVITYOPTIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.Fil: Gaspoz, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; ArgentinaFil: Kreuzer, Christian. Universität Dortmund; AlemaniaFil: Veeser, Andreas. Università degli Studi di Milano; ItaliaFil: Wollner, Winnifried. Universitat Hamburg; AlemaniaAmerican Institute of Mathematical Sciences2025-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/272429Gaspoz, Fernando Daniel; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried; A posteriori error analysis for optimization with PDE constraints; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 15; 4; 12-2025; 1346-13752156-84722156-8499CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org//article/doi/10.3934/mcrf.2025042info:eu-repo/semantics/altIdentifier/doi/10.3934/mcrf.2025042info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:25:34Zoai:ri.conicet.gov.ar:11336/272429instacron: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:34982025-10-29 12:25:35.075CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A posteriori error analysis for optimization with PDE constraints
title A posteriori error analysis for optimization with PDE constraints
spellingShingle A posteriori error analysis for optimization with PDE constraints
Gaspoz, Fernando Daniel
CONTROL
FINITE ELEMENTS
ADAPTIVITY
OPTIMIZATION
title_short A posteriori error analysis for optimization with PDE constraints
title_full A posteriori error analysis for optimization with PDE constraints
title_fullStr A posteriori error analysis for optimization with PDE constraints
title_full_unstemmed A posteriori error analysis for optimization with PDE constraints
title_sort A posteriori error analysis for optimization with PDE constraints
dc.creator.none.fl_str_mv Gaspoz, Fernando Daniel
Kreuzer, Christian
Veeser, Andreas
Wollner, Winnifried
author Gaspoz, Fernando Daniel
author_facet Gaspoz, Fernando Daniel
Kreuzer, Christian
Veeser, Andreas
Wollner, Winnifried
author_role author
author2 Kreuzer, Christian
Veeser, Andreas
Wollner, Winnifried
author2_role author
author
author
dc.subject.none.fl_str_mv CONTROL
FINITE ELEMENTS
ADAPTIVITY
OPTIMIZATION
topic CONTROL
FINITE ELEMENTS
ADAPTIVITY
OPTIMIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.
Fil: Gaspoz, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina
Fil: Kreuzer, Christian. Universität Dortmund; Alemania
Fil: Veeser, Andreas. Università degli Studi di Milano; Italia
Fil: Wollner, Winnifried. Universitat Hamburg; Alemania
description We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a posteriori bounds capturing the approximation of the state, the adjoint state, the control and the observation. The upper and lower bounds show a gap, which grows with decreasing cost or Tikhonov regularization parameter. This growth is mitigated compared to previous results and can be countered by refinement if control and observation involve compact operators. Numerical results illustrate these properties for model problems with distributed and boundary control.
publishDate 2025
dc.date.none.fl_str_mv 2025-12
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/11336/272429
Gaspoz, Fernando Daniel; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried; A posteriori error analysis for optimization with PDE constraints; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 15; 4; 12-2025; 1346-1375
2156-8472
2156-8499
CONICET Digital
CONICET
url http://hdl.handle.net/11336/272429
identifier_str_mv Gaspoz, Fernando Daniel; Kreuzer, Christian; Veeser, Andreas; Wollner, Winnifried; A posteriori error analysis for optimization with PDE constraints; American Institute of Mathematical Sciences; Mathematical Control and Related Fields; 15; 4; 12-2025; 1346-1375
2156-8472
2156-8499
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org//article/doi/10.3934/mcrf.2025042
info:eu-repo/semantics/altIdentifier/doi/10.3934/mcrf.2025042
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 American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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_ 1847427167628034048
score 12.589754

Publicaciones similares