dc.contributor.author Kosinka, J. dc.contributor.author Barton, M. dc.date.accessioned 2018-11-01T08:14:56Z dc.date.available 2018-11-01T08:14:56Z dc.date.issued 2018-10-31 dc.identifier.issn 0377-0427 dc.identifier.uri http://hdl.handle.net/20.500.11824/882 dc.description.abstract A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed en_US by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and n + 1 points that lie on the connecting lines between the barycentre and the vertices of the simplex. In the planar case, this particular rule belongs to a two-parameter family of quadrature rules that admit exact integration of bivariate polynomials of total degree three over triangles. We prove that this rule is exact for a larger space, namely the C1 cubic Clough-Tocher spline space over macro-triangles if and only if the split-point is the barycentre. This results into a factor of three reduction in the number of quadrature points needed to integrate the Clough-Tocher spline space exactly. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID ES/1PE/MTM2016-76329-R en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Journal of Computational and Applied Mathematics en_US
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