The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities
type: Item
instance of: scholarly article
title: The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities
zbMATH Open document ID: 0797.65083
author: V. Pereyra
published in: Journal of Computational Physics
publication date: 1994-10-09T00:00:00Z
review text: The method of auxiliary mapping (MAM) introduced by \textit{I. Babuška} and \textit{H.-S. Oh} [Numer. Methods Partial Differ. Equations 6, No. 4, 371-392 (1990; Zbl 0717.65084)], is applied to the homogeneous Laplace equation with boundary singularities and to the Helmholtz equation with both corner and boundary singularities. An exponential rate of convergence for the \(p\)-version of the finite element method (FEM) is proved. In addition, convergence estimates are proved for MAM applied to the \(h\)-\(p\) version of the FEM. Three benchmark problems are subject to numerical experiments comparing MAM with other FEM codes (PLTMG 6, FESOP), with ELLPACK, and the singular element code ISBFM. Errors and CPU time are compared graphically, as well.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 516917
zbMATH Keywords: PLTMG 6
zbMATH Keywords: FESOP
zbMATH Keywords: method of auxiliary mapping
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary singularities
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: exponential rate of convergence
zbMATH Keywords: \(p\)- version
zbMATH Keywords: \(h\)-\(p\) version
zbMATH Keywords: benchmark problems
zbMATH Keywords: numerical experiments
zbMATH Keywords: ELLPACK
zbMATH Keywords: ISBFM
reviewed by: Pavel Burda
describes a project that uses: PLTMG
describes a project that uses: ELLPACK
MaRDI profile type: Publication
full work available at URL: jcph.1993.1186
OpenAlex ID: W4255556467
DOI: 10.1006/JCPH.1993.1186
description: scientific article; zbMATH DE number 516917