On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs

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dc.contributor.author Bayona Revilla, Víctor
dc.contributor.author Flyer, Natasha
dc.contributor.author Fornberg, Bengt
dc.contributor.author Barnett, Gregory A.
dc.date.accessioned 2021-02-16T12:11:26Z
dc.date.available 2021-02-16T12:11:26Z
dc.date.issued 2017-03-01
dc.identifier.bibliographicCitation Bayona, V., Flyer, N., Fornberg, B., Barnett, G. A. (2017). On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs. Journal of Computational Physics, 332, 257–273.
dc.identifier.issn 0021-9991
dc.identifier.uri http://hdl.handle.net/10016/31935
dc.description.abstract RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs. We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions. In particular, the drawbacks on accuracy and stability due to Runge's phenomenon are overcome once the RBF stencils exceed a certain size due to an underlying minimization property. Test problems include the classical 2-D driven cavity, and also a 3-D global electric circuit problem with the earth's irregular topography as its bottom boundary. The results we find are fully consistent with previous results for data interpolation.
dc.description.sponsorship The National Center for Atmospheric Research is sponsored by the NSF. Victor Bayona was a post-doctoral fellow funded by the Advanced Study Program at the National Center for Atmospheric Research during the majority of this work.
dc.format.extent 17
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2017 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 Elliptic Pdes
dc.subject.other RBF-FD
dc.subject.other Polynomials
dc.subject.other Polyharmonic splines
dc.subject.other Runge's phenomenon
dc.subject.other Meshless
dc.title On the role of polynomials in RBF-FD approximations: II. numerical solution of elliptic PDEs
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.jcp.2016.12.008
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 257
dc.identifier.publicationlastpage 273
dc.identifier.publicationtitle Journal of Computational Physics
dc.identifier.publicationvolume 332
dc.identifier.uxxi AR/0000022054
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