TY - JOUR T1 - Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains AU - Graham , I.G. AU - Lin , Qun AU - Xie , Rui-Feng JO - Journal of Computational Mathematics VL - 3 SP - 231 EP - 244 PY - 1992 DA - 1992/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9356.html KW - AB -

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. 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 $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .