Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.11851/6286
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dc.contributor.authorAksoylu, Burak-
dc.contributor.authorBeyer, Horst Reinhard-
dc.contributor.authorÇeliker, Fatih-
dc.date.accessioned2021-09-11T15:35:38Z-
dc.date.available2021-09-11T15:35:38Z-
dc.date.issued2017en_US
dc.identifier.issn0163-0563-
dc.identifier.issn1532-2467-
dc.identifier.urihttps://doi.org/10.1080/01630563.2017.1320674-
dc.identifier.urihttps://hdl.handle.net/20.500.11851/6286-
dc.description.abstractWe study nonlocal equations from the area of peridynamics, an instance of nonlocal wave equation, and nonlocal diffusion on bounded domains whose governing equations contain a convolution operator based on integrals. We generalize the notion of convolution to accommodate local boundary conditions. On a bounded domain, the classical operator with local boundary conditions has a purely discrete spectrum, and hence, provides a Hilbert basis. We define an abstract convolution operator using this Hilbert basis, thereby automatically satisfying local boundary conditions. The main goal in this paper is twofold: apply the concept of abstract convolution operator to nonlocal problems and carry out a numerical study of the resulting operators. We study the corresponding initial value problems with prominent boundary conditions such as periodic, antiperiodic, Neumann, and Dirichlet. To connect to the standard convolution, we give an integral representation of the abstract convolution operator. For discretization, we use a weak formulation based on a Galerkin projection and use piecewise polynomials on each element which allows discontinuities of the approximate solution at the element borders. We study convergence order of solutions with respect to polynomial order and observe optimal convergence. We depict the solutions for each boundary condition.en_US
dc.description.sponsorshipNational Science FoundationNational Science Foundation (NSF) [DMS 1115280, DMS 1016190]; European CommissionEuropean CommissionEuropean Commission Joint Research Centre [DMS 1016190, 293978]; Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [MFAG 115F473]; TUBITAKTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2221]en_US
dc.description.sponsorshipBurak Aksoylu was supported in part by the National Science Foundation DMS 1016190 grant, European Commission Marie Curie Career Integration 293978 grant, and Scientific and Technological Research Council of Turkey (TUBITAK) MFAG 115F473 grant. Research visit of Horst R. Beyer was supported in part by the TUBITAK 2221 Fellowship for Visiting Scientist Program. Sabbatical visit of Fatih Celiker was supported in part by the TUBITAK 2221 Fellowship for Scientist on Sabbatical Leave Program.; Fatih Celiker was supported in part by the National Science Foundation DMS 1115280 grant.en_US
dc.language.isoenen_US
dc.publisherTaylor & Francis Incen_US
dc.relation.ispartofNumerical Functional Analysis And Optimizationen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBoundary conditionsen_US
dc.subjectGalerkin projection methoden_US
dc.subjectnonlocal operatoren_US
dc.subjectnonlocal wave equationen_US
dc.subjectoperator theoryen_US
dc.subjectperidynamicsen_US
dc.titleApplication and Implementation of Incorporating Local Boundary Conditions into Nonlocal Problemsen_US
dc.typeArticleen_US
dc.departmentFaculties, Faculty of Science and Literature, Department of Mathematicsen_US
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümütr_TR
dc.identifier.volume38en_US
dc.identifier.issue9en_US
dc.identifier.startpage1077en_US
dc.identifier.endpage1114en_US
dc.authorid0000-0002-7244-3340-
dc.authorid0000-0001-7570-780X-
dc.identifier.wosWOS:000406112300001en_US
dc.identifier.scopus2-s2.0-85020193054en_US
dc.institutionauthorAksoylu, Burak-
dc.identifier.doi10.1080/01630563.2017.1320674-
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.identifier.scopusqualityQ2-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextnone-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.cerifentitytypePublications-
item.languageiso639-1en-
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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