A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems
We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results...
- Autores:
-
Bastidas, Manuela
Lopez-Rodríguez, Bibiana
Osorio, Mauricio
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/25804
- Acceso en línea:
- http://hdl.handle.net/10784/25804
- Palabra clave:
- Hybridizable discontinuous Galerkin methods
flow in porous media
Dubiner’s basis
high order convergence
Método de Galerkin discontinuo hibridizable
flujo en medioporoso
bases de Dubiner
convergencia de alto orden
- Rights
- openAccess
- License
- Copyright © 2020 Manuela Bastidas, Bibiana Lopez-Rodríguez, Mauricio Osorio
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2020-11-112021-02-19T16:41:43Z2020-11-112021-02-19T16:41:43Z1794-9165http://hdl.handle.net/10784/25804We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results of existence and uniqueness of the weak and discontinuous solution of the second order elliptic equation, as well as the predicted convergence order of the HDG method. We highlight the use and implementation of Dubiner polynomial basis functions that allow us to develop a general and efficient high order numerical approximation. We also show some numerical examples that validate the theoretical results.En este artículo proponemos el uso del método de Galerkin discontinuo híbrido(HDG) para resolver un problema clásico en mecánica de fluidos: la ecuación deDarcy. Este modelo describe el comportamiento de un fluido a través de un medioporoso y es relevante en el estudio de flujo a gran escala. Aquí presentamos algunosresultados teóricos de existencia y unicidad de la solución débil y discontinua de ecuaciones elípticas de segundo orden, así como el orden de convergecia predichopara el método HDG. Destacamos el uso e implementación de bases polinomialesde Dubiner que nos permiten desarrollar aproximaciones numéricas generales yde alto orden. Además mostramos ejemplos numéricos que validan los resultadosteóricos.Palabras clave:Método de Galerkin discontinuo hibridizable; flujo en medioporoso; bases de Dubiner; convergencia de alto orden.application/pdfengUniversidad EAFIThttps://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6315/5060https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6315/5060Copyright © 2020 Manuela Bastidas, Bibiana Lopez-Rodríguez, Mauricio Osorioinfo:eu-repo/semantics/openAccessAcceso abiertohttp://purl.org/coar/access_right/c_abf2Revista Ingeniería y Ciencias, Vol. 16 Núm. 32 (2020)A High-Order HDG Method with Dubiner Basis for Elliptic Flow ProblemsMétodo HDG de orden superior con bases deDubiner para problemas de flujo elípticosarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Hybridizable discontinuous Galerkin methodsflow in porous mediaDubiner’s basishigh order convergenceMétodo de Galerkin discontinuo hibridizableflujo en medioporosobases de Dubinerconvergencia de alto ordenBastidas, ManuelaLopez-Rodríguez, BibianaOsorio, MauricioHasselt UniversityUniversidad Nacional de ColombiaIngeniería y Ciencias16323354THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/6273ac9f-babb-4975-9d29-db73d6664124/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINAL6315-Article Text-22597-1-10-20201113.pdf6315-Article Text-22597-1-10-20201113.pdfPDF Completoapplication/pdf3064225https://repository.eafit.edu.co/bitstreams/8573be4f-5bcf-4c2a-976c-60333d596bcd/downloadac575aacd51dfd714e2182f6fd8a8e52MD52articulo - copia (2).htmlarticulo - copia (2).htmlHTML Completotext/html375https://repository.eafit.edu.co/bitstreams/09262408-6758-4cda-b979-f2ad7bdb17b6/downloadfd5b377354fb0f6ceec60df0afa6a337MD5310784/25804oai:repository.eafit.edu.co:10784/258042021-04-28 22:02:35.328open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| dc.title.spa.fl_str_mv |
Método HDG de orden superior con bases deDubiner para problemas de flujo elípticos |
| title |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| spellingShingle |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems Hybridizable discontinuous Galerkin methods flow in porous media Dubiner’s basis high order convergence Método de Galerkin discontinuo hibridizable flujo en medioporoso bases de Dubiner convergencia de alto orden |
| title_short |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| title_full |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| title_fullStr |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| title_full_unstemmed |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| title_sort |
A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems |
| dc.creator.fl_str_mv |
Bastidas, Manuela Lopez-Rodríguez, Bibiana Osorio, Mauricio |
| dc.contributor.author.spa.fl_str_mv |
Bastidas, Manuela Lopez-Rodríguez, Bibiana Osorio, Mauricio |
| dc.contributor.affiliation.spa.fl_str_mv |
Hasselt University Universidad Nacional de Colombia |
| dc.subject.keyword.eng.fl_str_mv |
Hybridizable discontinuous Galerkin methods flow in porous media Dubiner’s basis high order convergence |
| topic |
Hybridizable discontinuous Galerkin methods flow in porous media Dubiner’s basis high order convergence Método de Galerkin discontinuo hibridizable flujo en medioporoso bases de Dubiner convergencia de alto orden |
| dc.subject.keyword.spa.fl_str_mv |
Método de Galerkin discontinuo hibridizable flujo en medioporoso bases de Dubiner convergencia de alto orden |
| description |
We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results of existence and uniqueness of the weak and discontinuous solution of the second order elliptic equation, as well as the predicted convergence order of the HDG method. We highlight the use and implementation of Dubiner polynomial basis functions that allow us to develop a general and efficient high order numerical approximation. We also show some numerical examples that validate the theoretical results. |
| publishDate |
2020 |
| dc.date.issued.none.fl_str_mv |
2020-11-11 |
| dc.date.available.none.fl_str_mv |
2021-02-19T16:41:43Z |
| dc.date.accessioned.none.fl_str_mv |
2021-02-19T16:41:43Z |
| dc.date.none.fl_str_mv |
2020-11-11 |
| dc.type.eng.fl_str_mv |
article info:eu-repo/semantics/article publishedVersion info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.local.spa.fl_str_mv |
Artículo |
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publishedVersion |
| dc.identifier.issn.none.fl_str_mv |
1794-9165 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10784/25804 |
| identifier_str_mv |
1794-9165 |
| url |
http://hdl.handle.net/10784/25804 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.isversionof.none.fl_str_mv |
https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6315/5060 |
| dc.relation.uri.none.fl_str_mv |
https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6315/5060 |
| dc.rights.eng.fl_str_mv |
Copyright © 2020 Manuela Bastidas, Bibiana Lopez-Rodríguez, Mauricio Osorio |
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http://purl.org/coar/access_right/c_abf2 |
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info:eu-repo/semantics/openAccess |
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Acceso abierto |
| rights_invalid_str_mv |
Copyright © 2020 Manuela Bastidas, Bibiana Lopez-Rodríguez, Mauricio Osorio Acceso abierto http://purl.org/coar/access_right/c_abf2 |
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openAccess |
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application/pdf |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees |
| dc.publisher.spa.fl_str_mv |
Universidad EAFIT |
| dc.source.spa.fl_str_mv |
Revista Ingeniería y Ciencias, Vol. 16 Núm. 32 (2020) |
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