(untitled) (Journal of Computational Mathematics, 1992)
The interior Dirichlet problem for Laplace's equation on a plane polygonal region Ω with boundary Γ may be reformulated as a second kind integral equation on Γ. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has O(n) points and is graded appropriately, then O(1/n^2) convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any xΩ. We present a simple extrapolation scheme which increases these rates of convergence to O(1/n^4) .