On structure of bivariate spline space of lower degree over arbitrary triangulation
type: Item
instance of: scholarly article
title: On structure of bivariate spline space of lower degree over arbitrary triangulation
zbMATH Open document ID: 1152.41007
author: Yu Liu
author: Zhongxuan Luo
author: Lijuan Chen
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-22T00:00:00Z
review text: Let \(\Delta \) be a triangulation of a planar polygon region. Let us denote by \(S_{k}^{\mu} (\Delta )\) the space of multivariate splines of degree \(k\) with smoothness order \(\mu \) over \(\Delta \). \textit{L. L. Schumaker} [Rocky Mt. J. Math. 14, 251--264 (1984; Zbl 0601.41034)] proposed a lower bound and an upper bound for the dimension of the space \(S_{k}^{\mu} (\Delta )\). In this paper the upper bound for \(\dim S_{k}^{\mu} (\Delta )\) given by Schumaker is slightly improved via the new vertex coding method. The authors also study the structure of the space \(S_{\mu}^{k}(\Delta) \) over arbitrary triangulation in the cases \(\mu = 1,\, k=2\) and \(3\).
reviewed by: Boris Golubov
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 5315381
zbMATH Keywords: bivariate spline
zbMATH Keywords: generator basis
zbMATH Keywords: structure matrix
zbMATH Keywords: matrix of generator basis
zbMATH Keywords: vertex coding
MaRDI profile type: Publication
full work available at URL: j.cam.2007.07.028
OpenAlex ID: W2023659726
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DOI: 10.1016/J.CAM.2007.07.028
description: scientific article; zbMATH DE number 5315381