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dc.contributor.authorKosinka, Jiří
dc.contributor.authorBarton, Michael
dc.date.accessioned2015-08-03T12:06:50Z
dc.date.available2015-08-03T12:06:50Z
dc.date.issued2014-08-08
dc.identifier.citationKosinka, J., & Bartoň, M. (2014). Convergence of Wachspress coordinates: from polygons to curved domains. Advances in Computational Mathematics, 41(3), 489–505. doi:10.1007/s10444-014-9370-3
dc.identifier.issn10197168
dc.identifier.doi10.1007/s10444-014-9370-3
dc.identifier.urihttp://hdl.handle.net/10754/563698
dc.description.abstractGiven a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases. © 2014 Springer Science+Business Media New York.
dc.publisherSpringer Nature
dc.subjectBarycentric coordinates
dc.subjectBarycentric mapping
dc.subjectConvergence
dc.subjectInterpolation
dc.titleConvergence of Wachspress coordinates: from polygons to curved domains
dc.typeArticle
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalAdvances in Computational Mathematics
dc.contributor.institutionComputer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD, United Kingdom
kaust.personBarton, Michael
dc.date.published-online2014-08-08
dc.date.published-print2015-06


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