Local energy estimates for the fractional Laplacian.
Resumen:
The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the numerical solutions. For finite element discretizations, we derive local error estimates in the Hs-seminorm and show optimal convergence rates in the interior of the domain by only assuming meshes to be shape-regular. These estimates quantify the fact that the reduced approximation error is concentrated near the boundary of the domain. We illustrate our theoretical results with several numerical examples.
| 2022 | |
| Juan Pablo Borthagaray ha sido financiado en parte por la beca DMS-1411808 de la NSF y la beca de viaje de AMS-Simons. | |
|
Finite elements Error estimates Interior error estimates Fractional Laplacian |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47829 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1877555092302856192 |
|---|---|
| author | Borthagaray, Juan Pablo |
| author2 | Leykekhman, Dmitriy Nochetto, Ricardo H. |
| author2_role | author author |
| author_facet | Borthagaray, Juan Pablo Leykekhman, Dmitriy Nochetto, Ricardo H. |
| author_role | author |
| bitstream.checksum.fl_str_mv | 6429389a7df7277b72b7924fdc7d47a9 a006180e3f5b2ad0b88185d14284c0e0 5499c15bd6b32c37160bfba5f71ab0a0 13adb202270a5f7cee03e795b33133c4 1d513dbaf09d9957d9835307dd904346 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 MD5 MD5 |
| bitstream.url.fl_str_mv | http://localhost:8080/xmlui/bitstream/20.500.12008/47829/5/license.txt http://localhost:8080/xmlui/bitstream/20.500.12008/47829/2/license_url http://localhost:8080/xmlui/bitstream/20.500.12008/47829/3/license_text http://localhost:8080/xmlui/bitstream/20.500.12008/47829/4/license_rdf http://localhost:8080/xmlui/bitstream/20.500.12008/47829/1/BLN22.pdf |
| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería. Leykekhman Dmitriy, University of Connecticut, USA Nochetto Ricardo H., University of Maryland, USA |
| dc.creator.none.fl_str_mv | Borthagaray, Juan Pablo Leykekhman, Dmitriy Nochetto, Ricardo H. |
| dc.date.accessioned.none.fl_str_mv | 2024-12-30T15:52:35Z |
| dc.date.available.none.fl_str_mv | 2024-12-30T15:52:35Z |
| dc.date.issued.none.fl_str_mv | 2022 |
| dc.description.abstract.none.fl_txt_mv | The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the numerical solutions. For finite element discretizations, we derive local error estimates in the Hs-seminorm and show optimal convergence rates in the interior of the domain by only assuming meshes to be shape-regular. These estimates quantify the fact that the reduced approximation error is concentrated near the boundary of the domain. We illustrate our theoretical results with several numerical examples. |
| dc.description.es.fl_txt_mv | También publicado en SIAM Journal on Numerical Analysis, vol. 59, no. 4, 2021, pp. 1918-1947. |
| dc.description.sponsorship.none.fl_txt_mv | Juan Pablo Borthagaray ha sido financiado en parte por la beca DMS-1411808 de la NSF y la beca de viaje de AMS-Simons. |
| dc.format.extent.es.fl_str_mv | 31 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Borthagaray, J., Leykekhman, D. y Nochetto, R. Local energy estimates for the fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2022, pp. 1-31. arXiv:2005.03786v2. |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/47829 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.none.fl_str_mv | Mathematics. Numerical Analysis (math.NA), arXiv:2005.03786v2, dec 2022, pp. 1-31. |
| 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 | Finite elements Error estimates Interior error estimates Fractional Laplacian |
| dc.title.none.fl_str_mv | Local energy estimates for the fractional Laplacian. |
| 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 | También publicado en SIAM Journal on Numerical Analysis, vol. 59, no. 4, 2021, pp. 1918-1947. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_0e8a704bdc1e319e538e3cf6747f34bd |
| identifier_str_mv | Borthagaray, J., Leykekhman, D. y Nochetto, R. Local energy estimates for the fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2022, pp. 1-31. arXiv:2005.03786v2. |
| 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:20.500.12008/47829 |
| publishDate | 2022 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@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 Ingeniería.Leykekhman Dmitriy, University of Connecticut, USANochetto Ricardo H., University of Maryland, USA2024-12-30T15:52:35Z2024-12-30T15:52:35Z2022Borthagaray, J., Leykekhman, D. y Nochetto, R. Local energy estimates for the fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2022, pp. 1-31. arXiv:2005.03786v2.https://hdl.handle.net/20.500.12008/47829También publicado en SIAM Journal on Numerical Analysis, vol. 59, no. 4, 2021, pp. 1918-1947.The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the numerical solutions. For finite element discretizations, we derive local error estimates in the Hs-seminorm and show optimal convergence rates in the interior of the domain by only assuming meshes to be shape-regular. These estimates quantify the fact that the reduced approximation error is concentrated near the boundary of the domain. We illustrate our theoretical results with several numerical examples.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2024-12-19T20:46:09Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BLN22.pdf: 703577 bytes, checksum: 1d513dbaf09d9957d9835307dd904346 (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2024-12-30T14:54:43Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BLN22.pdf: 703577 bytes, checksum: 1d513dbaf09d9957d9835307dd904346 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-12-30T15:52:35Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BLN22.pdf: 703577 bytes, checksum: 1d513dbaf09d9957d9835307dd904346 (MD5) Previous issue date: 2022Juan Pablo Borthagaray ha sido financiado en parte por la beca DMS-1411808 de la NSF y la beca de viaje de AMS-Simons.31 p.application/pdfenengarXivMathematics. Numerical Analysis (math.NA), arXiv:2005.03786v2, dec 2022, pp. 1-31.Las 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)Finite elementsError estimatesInterior error estimatesFractional LaplacianLocal energy estimates for the fractional Laplacian.Preprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBorthagaray, Juan PabloLeykekhman, DmitriyNochetto, Ricardo H.LICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/47829/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/47829/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; charset=utf-829882http://localhost:8080/xmlui/bitstream/20.500.12008/47829/3/license_text5499c15bd6b32c37160bfba5f71ab0a0MD53license_rdflicense_rdfapplication/rdf+xml; charset=utf-825790http://localhost:8080/xmlui/bitstream/20.500.12008/47829/4/license_rdf13adb202270a5f7cee03e795b33133c4MD54ORIGINALBLN22.pdfBLN22.pdfapplication/pdf703577http://localhost:8080/xmlui/bitstream/20.500.12008/47829/1/BLN22.pdf1d513dbaf09d9957d9835307dd904346MD5120.500.12008/478292024-12-30 12:52:35.605oai:colibri.udelar.edu.uy:20.500.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Institucionalhttps://www.colibri.udelar.edu.uyUniversidadhttps://udelar.edu.uy/https://www.colibri.udelar.edu.uy/oai/requestkarina.camps@seciu.edu.uyUruguayopendoar:47712024-12-30T15:52:35COLIBRI - Universidad de la Repúblicafalse |
| spellingShingle | Local energy estimates for the fractional Laplacian. Borthagaray, Juan Pablo Finite elements Error estimates Interior error estimates Fractional Laplacian |
| status_str | submittedVersion |
| title | Local energy estimates for the fractional Laplacian. |
| title_full | Local energy estimates for the fractional Laplacian. |
| title_fullStr | Local energy estimates for the fractional Laplacian. |
| title_full_unstemmed | Local energy estimates for the fractional Laplacian. |
| title_short | Local energy estimates for the fractional Laplacian. |
| title_sort | Local energy estimates for the fractional Laplacian. |
| topic | Finite elements Error estimates Interior error estimates Fractional Laplacian |
| url | https://hdl.handle.net/20.500.12008/47829 |
