Extrapolation For The Approximations To The Solution Of A Boundary Integral Equation On Polygonal Domains
Qun Lin 1, Rui-feng Xie 11 Institute of Systems Science, Academia Sinica, Beijing, China
Revised Online 2006-11-29
In this paper, we consider a boundary integral equation of second kind rising from potential theory. The equation may be solved numerically by Galerkin's method using piecewise constant functions. Because of the singularties produced by the corners, we have to grade the mesh near the corner. In general, Chandler obtained the order 2 superconvergence of the iterated Galerkin solution in the uniform norm. It is proved in this paper that the Richardson extrapolation increases the accuracy from order 2 to order 4.