Uniform Convergence Theorems of Boundary Solutions for Laplace's Equation

The numerical treatments for two-dimensional Laplace's equation with the Neumann condition are dealt with. The author gives a new numerical scheme for the boundary element methods to solve this problem. In this scheme, approximation for the domain is taken account of. The author gives also the uniform convergence theorem for this new scheme, and proves it rigorously. This new scheme is both mathematical and practical.