Finite element algorithms for nonlocal minimal graphs
Resumen:
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.
| 2022 | |
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Nonlocal minimal surfaces Finite elements Fractional diffusion |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/41307 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522802133106688 |
|---|---|
| author | Borthagaray, Juan Pablo |
| author2 | Li, Wenbo Nochetto, Ricardo |
| author2_role | author author |
| author_facet | Borthagaray, Juan Pablo Li, Wenbo Nochetto, Ricardo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Li Wenbo Nochetto Ricardo |
| dc.creator.none.fl_str_mv | Borthagaray, Juan Pablo Li, Wenbo Nochetto, Ricardo |
| dc.date.accessioned.none.fl_str_mv | 2023-11-17T17:25:42Z |
| dc.date.available.none.fl_str_mv | 2023-11-17T17:25:42Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems. |
| dc.format.extent.es.fl_str_mv | 29 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Borthagaray, J, Li, W y Nochetto, R. "Finite element algorithms for nonlocal minimal graphs". Mathematics in Engineering. [en línea] 2022, 4(2): 1–29. 29 h. DOI: 10.3934/mine.2022016 |
| dc.identifier.doi.none.fl_str_mv | 10.3934/mine.2022016 |
| dc.identifier.issn.none.fl_str_mv | 2640-3501 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/41307 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | AIMS Press |
| dc.relation.ispartof.es.fl_str_mv | Mathematics in Engineering, 2022, 4(2): 1–29 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Nonlocal minimal surfaces Finite elements Fractional diffusion |
| dc.title.none.fl_str_mv | Finite element algorithms for nonlocal minimal graphs |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | COLIBRI_54d6a93aaed02089d289ad37a1a3c455 |
| identifier_str_mv | Borthagaray, J, Li, W y Nochetto, R. "Finite element algorithms for nonlocal minimal graphs". Mathematics in Engineering. [en línea] 2022, 4(2): 1–29. 29 h. DOI: 10.3934/mine.2022016 2640-3501 10.3934/mine.2022016 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/41307 |
| publishDate | 2022 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Li WenboNochetto Ricardo2023-11-17T17:25:42Z2023-11-17T17:25:42Z2022Borthagaray, J, Li, W y Nochetto, R. "Finite element algorithms for nonlocal minimal graphs". Mathematics in Engineering. [en línea] 2022, 4(2): 1–29. 29 h. DOI: 10.3934/mine.20220162640-3501https://hdl.handle.net/20.500.12008/4130710.3934/mine.2022016We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.Submitted by Egaña Florencia (florega@gmail.com) on 2023-11-16T17:34:20Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 60f6c0b5ba35de03c3cfb9d4.pdf: 2565579 bytes, checksum: 6e58d19ddf5242914763c9973b3119f3 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-11-17T14:39:53Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 60f6c0b5ba35de03c3cfb9d4.pdf: 2565579 bytes, checksum: 6e58d19ddf5242914763c9973b3119f3 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-11-17T17:25:42Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 60f6c0b5ba35de03c3cfb9d4.pdf: 2565579 bytes, checksum: 6e58d19ddf5242914763c9973b3119f3 (MD5) Previous issue date: 202229 h.application/pdfenengAIMS PressMathematics in Engineering, 2022, 4(2): 1–29Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Nonlocal minimal surfacesFinite elementsFractional diffusionFinite element algorithms for nonlocal minimal graphsArtículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBorthagaray, Juan PabloLi, WenboNochetto, RicardoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/41307/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/41307/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Finite element algorithms for nonlocal minimal graphs Borthagaray, Juan Pablo Nonlocal minimal surfaces Finite elements Fractional diffusion |
| status_str | publishedVersion |
| title | Finite element algorithms for nonlocal minimal graphs |
| title_full | Finite element algorithms for nonlocal minimal graphs |
| title_fullStr | Finite element algorithms for nonlocal minimal graphs |
| title_full_unstemmed | Finite element algorithms for nonlocal minimal graphs |
| title_short | Finite element algorithms for nonlocal minimal graphs |
| title_sort | Finite element algorithms for nonlocal minimal graphs |
| topic | Nonlocal minimal surfaces Finite elements Fractional diffusion |
| url | https://hdl.handle.net/20.500.12008/41307 |
