A convergence rate theorem for finite difference approximations to delta functions
type: Item
instance of: scholarly article
title: A convergence rate theorem for finite difference approximations to delta functions
zbMATH Open document ID: 1155.65016
author: John D. Towers
published in: Journal of Computational Physics
publication date: 2008-07-21T00:00:00Z
review text: A new rate of convergence for approximations to certain integrals over codimension one manifolds in \(\mathbb R^n\), is proved. The type of manifold is defined by the zero level set of a smooth mapping \(u:\mathbb R^n\to\mathbb R\). The approximation method used, is based on two finite difference methods for the discretizing of the delta function, originally presented by the author in a previous research work [J. Comput. Phys. 220, No. 2, 915--931 (2007; Zbl 1115.65028)], were empirical convergence rates had indicated the first and second order accuracy. In this work these convergence rates are proved for the two proposed algorithms, under fairly general hypotheses.
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 5303107
zbMATH Keywords: delta function
zbMATH Keywords: integral
zbMATH Keywords: level set method
zbMATH Keywords: finite difference
zbMATH Keywords: approximation
zbMATH Keywords: regular grid
zbMATH Keywords: convergence rate
MaRDI profile type: Publication
full work available at URL: j.jcp.2008.03.019
OpenAlex ID: W2159881298
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DOI: 10.1016/J.JCP.2008.03.019
description: scientific article; zbMATH DE number 5303107