Numerical analysis on singular solutions of the Poisson equation in two-dimensions

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. This method is an extension of that presented in (Szabó and Yosibash 1996) to non-homogeneous boundary value problems, and is general in the sense that it is applicable to almost any type of point singularity. 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.