Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains (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 $x\in Ω$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .