Approximation of the derivatives of a function in Lagrange interpolation on low-dimensional simplices
type: Item
instance of: scholarly article
title: Approximation of the derivatives of a function in Lagrange interpolation on low-dimensional simplices
zbMATH Open document ID: 1464.41001
DOI: 10.1134/S008154382101017X
author: Yu. N. Subbotin
author: N. V. Baidakova
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2021-05-05T00:00:00Z
review text: When functions in one or more dimensions are approximated, there are a number of aspects to be considered: (i) from which space we approximate (in particular, when the dimension is more than one, we may wish to choose splines, radial basis functions, etc), (ii) how we approximate, especially interpolation or the very attractive so-called quasi-interpolation, (iii) whether function values of the approximant only are approximated or -- in Hermite-style -- derivatives as well. In all three choices, the resulting convergence orders are of particular interest. In this paper, new results for three and four dimensions are offered, especially when Lagrange interpolation is carried out on simplices. With respect to our question (ii), interpolations, pointwise, are taken, and in (iii) derivatives are approximated. Convergence orders are established, too. As an application, finite element methods are mentioned as well.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 7343923
zbMATH Keywords: multidimensional interpolation
zbMATH Keywords: finite element method
MaRDI profile type: Publication
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full work available at URL: s008154382101017x
OpenAlex ID: W3157764673
description: scientific article; zbMATH DE number 7343923