An insight into RBF-FD approximations augmented with polynomials

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dc.contributor.author Bayona Revilla, Víctor
dc.date.accessioned 2021-02-16T13:05:48Z
dc.date.available 2021-05-01T23:00:07Z
dc.date.issued 2019-05-01
dc.identifier.bibliographicCitation Bayona, V. (2019). An insight into RBF-FD approximations augmented with polynomials. Computers & Mathematics with Applications, 77(9), 2337–2353
dc.identifier.issn 0898-1221
dc.identifier.uri http://hdl.handle.net/10016/31939
dc.description.abstract Radial basis function-generated finite differences (RBF-FD) based on the combination of polyharmonic splines (PHS) with high degree polynomials have recently emerged as a powerful and robust numerical approach for the local interpolation and derivative approximation of functions over scattered node layouts. Among the key features, (i) high orders of accuracy can be achieved without the need of selecting a shape parameter or the issues related to numerical ill-conditioning, and (ii) the harmful edge effects associated to the use of high order polynomials (better known as Runge's phenomenon) can be overcome by simply increasing the stencil size for a fixed polynomial degree. The present study complements our previous results, providing an analytical insight into RBF-FD approximations augmented with polynomials. It is based on a closed-form expression for the interpolant, which reveals the mechanisms underlying these features, including the role of polynomials and RBFs in the interpolant, the approximation error, and the behavior of the cardinal functions near boundaries. Numerical examples are included for illustration.
dc.format.extent 17
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2019 Elsevier
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other RBF
dc.subject.other RBF-FD
dc.subject.other Polynomials
dc.subject.other Interpolation
dc.subject.other Meshfree
dc.subject.other Runge's phenomenon
dc.subject.other Radial basis functions
dc.subject.other Finite-differences
dc.subject.other Interpolation
dc.subject.other Quadrature
dc.title An insight into RBF-FD approximations augmented with polynomials
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.camwa.2018.12.029
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. FIS2016-77892-R
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 2337
dc.identifier.publicationissue 9
dc.identifier.publicationlastpage 2353
dc.identifier.publicationtitle Computers & Mathematics with Applications
dc.identifier.publicationvolume 77
dc.identifier.uxxi AR/0000022547
dc.contributor.funder Ministerio de Ciencia e Innovación (España)
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