\(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
type: Item
instance of: scholarly article
title: \(C^ r\)-finite elements of Powell-Sabin type on the three direction mesh
zbMATH Open document ID: 0867.65002
DOI: 10.1007/BF02127703
published in: Advances in Computational Mathematics
publication date: 1997-07-13T00:00:00Z
review text: The triangulation \(\tau\) generated by a uniform three direction mesh of the plane and the Powell-Sabin subtriangulation \(\tau_6\) obtained by subdividing each triangle \(T\in\tau\) by connecting each vertex to the midpoint of the opposite side are considered. The existence of Hermite interpolation schemes in a subspace of \(S^r_n (\tau_6)\) for lower degrees (i.e. \(n=2r+1\) for \(r\) even and \(n=2r\) for \(r\) odd) is proven. Some results on the Bernstein-Bézier form of polynomials on triangles which is used for representing splines on the triangulation \(\tau_6\) are given. The construction of Powell-Sabin finite elements and the solution of the Hermite interpolation problem of order \(r\) are discussed. The interpolation error is estimated.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 989553
zbMATH Keywords: splines
zbMATH Keywords: finite elements
zbMATH Keywords: Bernstein-Bézier polynomial
zbMATH Keywords: triangulation
zbMATH Keywords: three direction mesh
zbMATH Keywords: Powell-Sabin subtriangulation
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: Powell-Sabin finite elements
author: Mohammed Laghchim-Lahlou
author: P. Sablonnière
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02127703
OpenAlex ID: W2009536953
description: scientific article; zbMATH DE number 989553