Comparison of two methods for the computation of singular solutions in elliptic problems

Georgiou, G; Boudouvis, A; Poullikkas, A

dc.contributor.author	Georgiou, G	en
dc.contributor.author	Boudouvis, A	en
dc.contributor.author	Poullikkas, A	en
dc.date.accessioned	2014-03-01T01:12:41Z
dc.date.available	2014-03-01T01:12:41Z
dc.date.issued	1997	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12206
dc.subject	Convergence	en
dc.subject	Elliptic problems	en
dc.subject	Singularities	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Approximation theory	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Finite element method	en
dc.subject.other	Integral equations	en
dc.subject.other	Lagrange multipliers	en
dc.subject.other	Polynomials	en
dc.subject.other	Integrated singular basis function method (ISBFM)	en
dc.subject.other	Boundary value problems	en
dc.title	Comparison of two methods for the computation of singular solutions in elliptic problems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0377-0427(96)00173-2	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0377-0427(96)00173-2	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	We compare two numerical methods for the solution of elliptic problems with boundary singularities. The first is the integrated singular basis function method (ISBFM), a finite-element method in which the solution is approximated by standard polynomial basis functions supplemented by the leading terms of the local (singular) solution expansion. A double application of Green's theorem reduces all Galerkin integrals containing singular terms to boundary integrals with nonsingular integrands. The originally essential boundary conditions are weakly enforced by means of Lagrange multipliers. The second method is a singular function boundary integral method which can be viewed as a modification of the ISBFM. The solution is approximated only by the leading terms of the local solution expansion. The discretized equations are boundary integrals and the dimension of the problem is reduced by one. The two methods are applied to the cracked-beam problem giving very accurate estimates of the leading singular coefficients. Comparisons are made and their limitations are discussed.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/S0377-0427(96)00173-2	en
dc.identifier.isi	ISI:A1997WV12800009	en
dc.identifier.volume	79	en
dc.identifier.issue	2	en
dc.identifier.spage	277	en
dc.identifier.epage	287	en