On the finite element method for a singular problem
type: Item
instance of: scholarly article
title: On the finite element method for a singular problem
zbMATH Open document ID: 0757.65113
DOI: 10.1016/0096-3003(92)90027-X
author: A. R. M. El-Namoury
published in: Applied Mathematics and Computation
publication date: 1992-09-27T00:00:00Z
review text: The paper is concerned with a finite element method for a boundary value problem with Laplace's equation on a slotted rectangle. In order to cover the singularity of the exact solution, an expansion into a series of `` singular functions'' (with increasing degree of smoothness) is used to obtain a suitable set of basis functions for a finite element method with triangular elements: It consists of the ``usual'' piecewise linear functions and some of the singular functions. It is shown that the method converges linearly. A numerical example indicates that two singular functions in the basis are enough.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 64332
zbMATH Keywords: singular problem
zbMATH Keywords: slotted domain
zbMATH Keywords: linear convergence
zbMATH Keywords: finite element method
zbMATH Keywords: Laplace equation
zbMATH Keywords: singular functions
zbMATH Keywords: numerical example
reviewed by: Michael Plum
MaRDI profile type: Publication
cites work: Direct and inverse error estimates for finite elements with mesh refinements
cites work: Q3831326
cites work: Q5643544
cites work: The use of infinite grid refinements at singularities in the solution of Laplace's equation
cites work: Singular Isoparametric Finite Elements
cites work: Corner singularities in elliptic problems by finite element methods
full work available at URL: 0096-3003(92)90027-x
OpenAlex ID: W1982005891
description: scientific article; zbMATH DE number 64332