Finite element approximation of fractional Neumann problems
Resumen:
In this paper, we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method’s performance as well as certain properties of solutions.
| 2022 | |
|
Numerical analysis Neumann boundary condition Fractional Laplacian |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38861 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522797257228288 |
|---|---|
| author | Borthagaray, Juan Pablo |
| author2 | Bersetche, Francisco |
| author2_role | author |
| author_facet | Borthagaray, Juan Pablo Bersetche, Francisco |
| 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 Matemáticas. Bersetche Francisco |
| dc.creator.none.fl_str_mv | Borthagaray, Juan Pablo Bersetche, Francisco |
| dc.date.accessioned.none.fl_str_mv | 2023-08-02T13:01:09Z |
| dc.date.available.none.fl_str_mv | 2023-08-02T13:01:09Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | In this paper, we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method’s performance as well as certain properties of solutions. |
| dc.description.es.fl_txt_mv | Publicado también en: IMA Journal of Numerical Analysis, 2022, 42(4): 3207–3240. DOI: 10.1093/imanum/drab064 |
| 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 y Bersetche, F. "Finite element approximation of fractional Neumann problems" [Preprint]. Publicado en: Mathematics (Numerical Analysis). 2022, arXiv: 2008.06129, Dic 2022, pp. 1-29. DOI: 10.48550/arXiv.2105.06079 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2105.06079 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/38861 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Numerical Analysis). 2022, arXiv: 2008.06129, Dic 2022, pp. 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 | Numerical analysis Neumann boundary condition Fractional Laplacian |
| dc.title.none.fl_str_mv | Finite element approximation of fractional Neumann problems |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Publicado también en: IMA Journal of Numerical Analysis, 2022, 42(4): 3207–3240. DOI: 10.1093/imanum/drab064 |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_bead4b3af21e9a657e633ed073d0bfb0 |
| identifier_str_mv | Borthagaray, J y Bersetche, F. "Finite element approximation of fractional Neumann problems" [Preprint]. Publicado en: Mathematics (Numerical Analysis). 2022, arXiv: 2008.06129, Dic 2022, pp. 1-29. DOI: 10.48550/arXiv.2105.06079 10.48550/arXiv.2105.06079 |
| 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:20.500.12008/38861 |
| 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 Matemáticas.Bersetche Francisco2023-08-02T13:01:09Z2023-08-02T13:01:09Z2022Borthagaray, J y Bersetche, F. "Finite element approximation of fractional Neumann problems" [Preprint]. Publicado en: Mathematics (Numerical Analysis). 2022, arXiv: 2008.06129, Dic 2022, pp. 1-29. DOI: 10.48550/arXiv.2105.06079https://hdl.handle.net/20.500.12008/3886110.48550/arXiv.2105.06079Publicado también en: IMA Journal of Numerical Analysis, 2022, 42(4): 3207–3240. DOI: 10.1093/imanum/drab064In this paper, we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method’s performance as well as certain properties of solutions.Submitted by Egaña Florencia (florega@gmail.com) on 2023-08-01T21:01:31Z No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2008.06129.pdf: 1085053 bytes, checksum: 706867905206d51513c07309bc00a978 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2023-08-02T11:23:28Z (GMT) No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2008.06129.pdf: 1085053 bytes, checksum: 706867905206d51513c07309bc00a978 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2023-08-02T13:01:09Z (GMT). No. of bitstreams: 2 license_rdf: 23149 bytes, checksum: 1996b8461bc290aef6a27d78c67b6b52 (MD5) 2008.06129.pdf: 1085053 bytes, checksum: 706867905206d51513c07309bc00a978 (MD5) Previous issue date: 202229 h.application/pdfenengarXivMathematics (Numerical Analysis). 2022, arXiv: 2008.06129, Dic 2022, pp. 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)Numerical analysisNeumann boundary conditionFractional LaplacianFinite element approximation of fractional Neumann problemsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBorthagaray, Juan PabloBersetche, FranciscoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/38861/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/38861/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Finite element approximation of fractional Neumann problems Borthagaray, Juan Pablo Numerical analysis Neumann boundary condition Fractional Laplacian |
| status_str | submittedVersion |
| title | Finite element approximation of fractional Neumann problems |
| title_full | Finite element approximation of fractional Neumann problems |
| title_fullStr | Finite element approximation of fractional Neumann problems |
| title_full_unstemmed | Finite element approximation of fractional Neumann problems |
| title_short | Finite element approximation of fractional Neumann problems |
| title_sort | Finite element approximation of fractional Neumann problems |
| topic | Numerical analysis Neumann boundary condition Fractional Laplacian |
| url | https://hdl.handle.net/20.500.12008/38861 |
