Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity
Ημερομηνία
2012Συγγραφέας
Christodoulou, Evgenia![ORCID logo](https://orcid.org/sites/default/files/images/orcid_16x16.png)
![ORCID logo](https://orcid.org/sites/default/files/images/orcid_16x16.png)
![ORCID logo](https://orcid.org/sites/default/files/images/orcid_16x16.png)
ISSN
0749-159XSource
Numerical Methods for Partial Differential EquationsVolume
28Issue
3Pages
749-767Google Scholar check
Keyword(s):
Metadata
Εμφάνιση πλήρους εγγραφήςΕπιτομή
In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution, and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. By means of Green's theorem, the resulting discretized equations are posed and solved on the boundary of the domain, away from the point where the singularity arises. We analyze the convergence of the method and prove that the coefficients in the local asymptotic expansion, also referred to as stress intensity factors, are approximated at an exponential rate as the number of the employed expansion terms is increased. Our theoretical results are illustrated through a numerical experiment. Copyright © 2011 Wiley Periodicals, Inc.
Collections
Cite as
Related items
Showing items related by title, author, creator and subject.
-
Article
The Singular Function Boundary Integral Method for singular Laplacian problems over circular sections
Christodoulou, Evgenia; Xenophontos, Christos A.; Georgiou, Georgios C. (2010)The Singular Function Boundary Integral Method (SFBIM) for solving two-dimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic ...
-
Article
The singular function boundary integral method for 3-D Laplacian problems with a boundary straight edge singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Xenophontos, Christos A.; Georgiou, Georgios C. (2012)Three-dimensional Laplace problems with a boundary straight-edge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...
-
Article
The singular function boundary integral method for biharmonic problems with crack singularities
Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2007)We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, ...