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dc.contributor.authorKosinka, J.
dc.contributor.authorBarton, M. 
dc.date.accessioned2018-11-01T08:14:56Z
dc.date.available2018-11-01T08:14:56Z
dc.date.issued2018-10-31
dc.identifier.issn0377-0427
dc.identifier.urihttp://hdl.handle.net/20.500.11824/882
dc.description.abstractA numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed 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.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleGaussian quadrature for $C^1$ cubic Clough-Tocher macro-trianglesen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDES/1PE/MTM2016-76329-Ren_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleJournal of Computational and Applied Mathematicsen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España