On the convergence of the vortex loop method with regularization for the Neumann boundary value problem on a plane screen
type: Item
instance of: scholarly article
title: On the convergence of the vortex loop method with regularization for the Neumann boundary value problem on a plane screen
zbMATH Open document ID: 1237.65135
DOI: 10.1134/S0012266111090138
author: G. V. Ryzhakov
author: A. V. Setukha
published in: Differential Equations
publication date: 2012-01-18T00:00:00Z
review text: The Laplace equation in \(\mathbb{R}^3\) along with Neumann conditions on a finite plane surface \(\Sigma\) is considered for Hölder-continuous Neumann data (with Hölder exponent \(\alpha\)). This exterior boundary value problem is reduced to a singular integral equation on \(\Sigma\) the singularity of which is understood in the Hadamard sense. A collocation method for the numerical solution of this integral equation is proposed which uses a partition of \(\Sigma\) into finite elements, and piecewise constant basis functions. (The physical interpretation of this approach leads to the name of the method mentioned in the title.) The authors prove the uniform convergence of their approach and obtain an error estimate in case \(\alpha>\frac12\).
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 5998581
zbMATH Keywords: Laplace equation
zbMATH Keywords: Neumann problem
zbMATH Keywords: singular integral equation
zbMATH Keywords: collocation method
zbMATH Keywords: error bound
zbMATH Keywords: finite element
zbMATH Keywords: convergence
zbMATH Keywords: exterior boundary value problem
MaRDI profile type: Publication
cites work: Q4390414
cites work: On the convergence of a numerical method for a hypersingular integral equation on a closed surface
description: scientific article; zbMATH DE number 5998581