AN ACCURATE SEMIANALYTIC FINITE-DIFFERENCE SCHEME FOR 2-DIMENSIONAL ELLIPTIC PROBLEMS WITH SINGULARITIES

A high-order semi-analytic finite difference scheme is presented to ov ercome degradation of numerical performance when applied to two-dimens ional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional representation of the exact solution in the vicin ity of the singularities, and a conventional finite difference scheme on the remaining domain. It is shown that the L-S SFDS is ''pollution' ' free, i.e., no degradation in the convergence rate occurs because of the singularities, and the coefficients of the asymptotic solution in the vicinity of the singularities are computed as a by-product with a very high accuracy. Numerical examples for the Laplace and Poisson eq uations over domains containing re-entrant corners or abrupt changes i n the boundary conditions are presented. (C) 1998 John Wiley & Sons, I nc.