Numerical analysis on singular solutions of the Poisson equation in two dimensions (Q1376215)

A numerical method for extracting the coefficients of the asymptotic series solution of the Poisson equation in two dimensions in the vicinity of singular points is presented. Numerical experiments for crack-tip singularities, re-entrant corner singularities, abrupt change in boundary conditions, and singularities associated with a multi-material inclusion are presented to substantiate the proposed techniques. Constant as well as varying non-homogeneous ``right-hand-side'' functions are studied.