Gradient method with AFEM for parameter-estimation
Descripción del Articulo
We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on the finite-dimensional parameter space for the minimization of the least-squares residual. Since the gradient involve...
| Autor: | |
|---|---|
| Formato: | artículo |
| Fecha de Publicación: | 2023 |
| Institución: | Universidad Nacional de Trujillo |
| Repositorio: | Revistas - Universidad Nacional de Trujillo |
| Lenguaje: | inglés |
| OAI Identifier: | oai:ojs.revistas.unitru.edu.pe:article/5281 |
| Enlace del recurso: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281 |
| Nivel de acceso: | acceso abierto |
| Materia: | Adaptive finite element methods parameter estimation gradient method |
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Gradient method with AFEM for parameter-estimationBecker, RolandAdaptive finite element methodsparameter estimationgradient methodWe consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on the finite-dimensional parameter space for the minimization of the least-squares residual. Since the gradient involves solution of partial differential equations, it is not accesable, and is replaced by an approximation obtained by finite elements. This results into a perturbed gradient method. We use an (a posteriori) error estimator to control the accuracy of the gradient approximation and propose an algorithm, which links the estimator to the progress of the iteration. We show convergence of the algorithm under typical structural assumptions.National University of Trujillo - Academic Department of Mathematics2023-06-14info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281Selecciones Matemáticas; Vol. 10 No. 01 (2023): Special Issue; 51 - 59Selecciones Matemáticas; Vol. 10 Núm. 01 (2023): Special Issue; 51 - 59Selecciones Matemáticas; v. 10 n. 01 (2023): Special Issue; 51 - 592411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUenghttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281/5449https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/52812023-06-20T21:59:24Z |
| dc.title.none.fl_str_mv |
Gradient method with AFEM for parameter-estimation |
| title |
Gradient method with AFEM for parameter-estimation |
| spellingShingle |
Gradient method with AFEM for parameter-estimation Becker, Roland Adaptive finite element methods parameter estimation gradient method |
| title_short |
Gradient method with AFEM for parameter-estimation |
| title_full |
Gradient method with AFEM for parameter-estimation |
| title_fullStr |
Gradient method with AFEM for parameter-estimation |
| title_full_unstemmed |
Gradient method with AFEM for parameter-estimation |
| title_sort |
Gradient method with AFEM for parameter-estimation |
| dc.creator.none.fl_str_mv |
Becker, Roland |
| author |
Becker, Roland |
| author_facet |
Becker, Roland |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Adaptive finite element methods parameter estimation gradient method |
| topic |
Adaptive finite element methods parameter estimation gradient method |
| description |
We consider the adaptive finite element discretization of parameter estimation problems for nonlinear elliptic partial differential equations. The idea is to use a gradient method on the finite-dimensional parameter space for the minimization of the least-squares residual. Since the gradient involves solution of partial differential equations, it is not accesable, and is replaced by an approximation obtained by finite elements. This results into a perturbed gradient method. We use an (a posteriori) error estimator to control the accuracy of the gradient approximation and propose an algorithm, which links the estimator to the progress of the iteration. We show convergence of the algorithm under typical structural assumptions. |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023-06-14 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281 |
| url |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/5281/5449 |
| dc.rights.none.fl_str_mv |
https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| publisher.none.fl_str_mv |
National University of Trujillo - Academic Department of Mathematics |
| dc.source.none.fl_str_mv |
Selecciones Matemáticas; Vol. 10 No. 01 (2023): Special Issue; 51 - 59 Selecciones Matemáticas; Vol. 10 Núm. 01 (2023): Special Issue; 51 - 59 Selecciones Matemáticas; v. 10 n. 01 (2023): Special Issue; 51 - 59 2411-1783 reponame:Revistas - Universidad Nacional de Trujillo instname:Universidad Nacional de Trujillo instacron:UNITRU |
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Universidad Nacional de Trujillo |
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UNITRU |
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UNITRU |
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Revistas - Universidad Nacional de Trujillo |
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Revistas - Universidad Nacional de Trujillo |
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1845886946819178496 |
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13.361153 |
Nota importante:
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
La información contenida en este registro es de entera responsabilidad de la institución que gestiona el repositorio institucional donde esta contenido este documento o set de datos. El CONCYTEC no se hace responsable por los contenidos (publicaciones y/o datos) accesibles a través del Repositorio Nacional Digital de Ciencia, Tecnología e Innovación de Acceso Abierto (ALICIA).
