Smooth macro-elements based on Clough-Tocher triangle splits
type: Item
instance of: scholarly article
title: Smooth macro-elements based on Clough-Tocher triangle splits
zbMATH Open document ID: 0998.65016
author: Peter Alfeld
author: Larry L. Schumaker
published in: Numerische Mathematik
publication date: 2002-05-21T00:00:00Z
review text: A bivariate macro-element defined on a triangle consists of a finite dimensional linear-space \(\mathcal S\) defined on the triangle and a set of linear functionals forming a basis for the dual of \(\mathcal S\). A macro-element defines a local interpolation scheme. The first \({\mathcal C}^r\) macro-elements were constructed using polynomials of degree \(4r+1\). To get macro-elements using lower degree polynomials, it is necesssary to split the triangle. In the present paper, macro-elements of smoothness \({\mathcal C}^r\) on Clough-Tocher triangle splits are constructed for all \(r\geq 0\). These new elements are improvements on elements constructed in a paper by \textit{M. J. Lai} and \textit{L. L. Schumaker} [ibid. 88, No.~1, 105-119 (2001; Zbl 0989.65013)]. The application of the new elements to Hermite interpolation of scattered data is described and numerical experiments are given.
reviewed by: Heiner Mühlig
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1742790
zbMATH Keywords: bivariate approximation
zbMATH Keywords: splines
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: bivariate macro-element
zbMATH Keywords: Clough-Tocher triangle splits
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s002110100304
OpenAlex ID: W2029096786
DOI: 10.1007/S002110100304
description: scientific article; zbMATH DE number 1742790