Local Lagrange interpolation by quintic \(C^1\) splines on type-6 tetrahedral partitions
type: Item
instance of: scholarly article
title: Local Lagrange interpolation by quintic \(C^1\) splines on type-6 tetrahedral partitions
zbMATH Open document ID: 1231.65025
author: M. Rhein
author: Günther Nürnberger
author: Georg Schneider
published in: Journal of Computational and Applied Mathematics
publication date: 2011-12-08T00:00:00Z
review text: Piecewise polynomial splines in three dimensions are defined with which interpolation can be carried out. The splines are of degree five and defined on tetrahedra. The individual polynomial pieces are joined so that the complete spline is differentiable. The interpolation is of Lagrange type and the authors show existence and uniqueness for the interpolants for the given data. As a consequence, the interpolation scheme is local and has linear complexity. They also show stability and include an approximation order theorem. The latter bounds the uniform error on a compact polyhedral domain by a multiple of \(h^{m+1}\), where \(h\) is the length of the edges of the cube partition and \(m\) is at most five. Further, derivatives of the approximation error are bounded, too.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 5987773
zbMATH Keywords: trivariate splines
zbMATH Keywords: approximation order
zbMATH Keywords: error bounds
zbMATH Keywords: interpolation
zbMATH Keywords: linear complexity
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.cam.2011.07.029
OpenAlex ID: W81081493
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DOI: 10.1016/J.CAM.2011.07.029
description: scientific article; zbMATH DE number 5987773