High Order Fast Laplace Solvers for the Dirichlet Problem on General Regions
Victor L. Pereyra, Włodzimierz Proskurowski, Olof B. Widlund · Mathematics of Computation · 1977
Highly accurate finite difference schemes are developed for Laplace’s equation with the Dirichlet boundary condition on general bounded regions in ${R^n}$. A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size