An iteration method using artificial boundary for some elliptic boundary value problems with singularities

By using an arti cial boundary an iteration method is designed to solve some elliptic boundary value problems with singularities. At each step of the iteration the standard nite element method is used to solve the problems in a domain without singularities. It is shown that the iteration method is equivalent to a Schwarz alternating method. Some numerical examples are given, which show the e ectiveness of the iteration method.