A \(C^r\) trivariate macro-element based on the Worsey-Farin split of a tetrahedron
type: Item
instance of: scholarly article
title: A \(C^r\) trivariate macro-element based on the Worsey-Farin split of a tetrahedron
zbMATH Open document ID: 1267.41011
author: Michael A. Matt
published in: Numerische Mathematik
publication date: 2013-02-25T00:00:00Z
review text: A superspline space on a special tetrahedral refinement of any arbitrary tetrahedral partition is considered. The tetrahedral refinement is called the Worsey-Farin refinement scheme and consist of splitting each tetrahedron of a partition into twelve subtetrahedra, which involves splitting each face with the well known bivariate Clough-Tocher split. The trivariate \(C^r\) macro-elements for any \(r\geq 1\) over the Worsey-Farin refinement of any tetrahedral partition are constructed. This extends the construction of \(C^1\) cubic Worsey-Farin elements and \(C^2\) elements of degree nine to the \(C^r\) situation with \(r>2\). It is shown that the degree of the polynomials used for proposed the macro-elements is the lowest.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 6138629
zbMATH Keywords: spline approximation
zbMATH Keywords: interpolation
zbMATH Keywords: splines
zbMATH Keywords: tetrahedral refinement scheme
zbMATH Keywords: macro-elements
reviewed by: V. L. Leontiev
MaRDI profile type: Publication
full work available at URL: s00211-012-0478-4
OpenAlex ID: W2035002140
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DOI: 10.1007/S00211-012-0478-4
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description: scientific article; zbMATH DE number 6138629