A singular function boundary integral method for laplacian problems with boundary singularities
Ημερομηνία
2006ISSN
1064-8275Source
SIAM Journal on Scientific ComputingVolume
28Issue
2Pages
517-532Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
A singular function boundary integral method for Laplacian problems with boundary singularities is analyzed. In this method, the solution is approximated by the truncated asymptotic expansion for the solution near the singular point and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. The resulting discrete problem is posed and solved on the boundary of the domain, away from the point of singularity. The main result of this paper is the proof of convergence of the method in particular, we show that the method approximates the generalized stress intensity factors, i.e., the coefficients in the asymptotic expansion, at an exponential rate. A numerical example illustrating the convergence of the method is also presented. © 2006 Society for Industrial and Applied Mathematics.
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