Comparison of two methods for the computation of singular solutions in elliptic problems
type: Item
instance of: scholarly article
title: Comparison of two methods for the computation of singular solutions in elliptic problems
zbMATH Open document ID: 0880.65083
DOI: 10.1016/S0377-0427(96)00173-2
author: A. Poullikkas
author: Georgios C. Georgiou
author: A. G. Boudouvis
published in: Journal of Computational and Applied Mathematics
publication date: 1998-01-08T00:00:00Z
review text: Specific properties of two methods for numerically solving elliptic problems with boundary singularities are compared by applying them both to the cracked beam problem. The methods have been analyzed in two previous papers in joint work by the first author. The first method is the integrated singular basis function method (ISBFM), while the second can be viewed as a variant of it. Both methods are finite element methods; with ISBFM, both the regular and singular part of the solution are approximated near the singularity, whereas with the second method, called singular function boundary integral method, only the singular part is approximated. The two methods prove to be accurate in estimating the leading singular coefficients; ISBFM is more stable and accurate, except for the second and third singular coefficients, because of the regular part approximation; on the other hand, the singular function boundary integral method is less costly to apply.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1022224
zbMATH Keywords: Elliptic problems
zbMATH Keywords: Boundary singularities
zbMATH Keywords: Cracked beam problem
zbMATH Keywords: stability
zbMATH Keywords: integrated singular basis function method
zbMATH Keywords: finite element methods
zbMATH Keywords: singular function boundary integral method
reviewed by: Juan Pedro Milaszewicz
MaRDI profile type: Publication
cites work: On grid refinement at point singularities forh-p methods
cites work: The integrated singular basis function method for the stick‐slip and the die‐swell problems
cites work: Q4869514
cites work: Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
cites work: A comparison of adaptive refinement techniques for elliptic problems
cites work: An efficient finite element method for treating singularities in Laplace's equation
cites work: An efficient method for subtracting off singularities at corners for Laplace's equation
description: scientific article; zbMATH DE number 1022224