TY - JOUR
T1 - Extrapolation of Nystrom Solutions of Boundary Integral Equations on Non-Smooth Domains
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 Nystrom 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 $O(1/n^4)$ .