``Approximate approximations'' and the cubature of potentials
type: Item
instance of: scholarly article
title: ``Approximate approximations'' and the cubature of potentials
zbMATH Open document ID: 0845.65008
author: Gunther Schmidt
author: V. Maz'ya
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1996-09-09T00:00:00Z
full work available at URL: https://eudml.org/doc/244089
review text: A new method is given for the approximation of singular integrals that arise in potential theory. The basic idea is to approximate the integrand using quasi interpolants constructed using integrand values at points on a regular mesh. The basis functions for the interpolation are products of generalized Laguerre polynomials and a Gaussian weight. For harmonic, elastic and diffraction potentials, this choice of basis function allows the authors to derive explicit formulas for the approximations to the singular integrals. Error analysis is given which provides error bounds for these basis functions, and more general basis functions. Some numerical results are given for the harmonic potential.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 852040
zbMATH Keywords: approximate approximations
zbMATH Keywords: cubature of potentials
zbMATH Keywords: error analysis
zbMATH Keywords: singular integrals
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Gaussian weight
zbMATH Keywords: error bounds
zbMATH Keywords: numerical results
zbMATH Keywords: harmonic potential
reviewed by: A. Genz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 852040