A high-order compact formulation for the 3D Poisson equation

In this work we construct an extension to a class of higher-order compact methods for the three-dimensional Poisson equation. A superconvergent nodal rate of O(h6) is predicted, or O(h4) if the forcing function derivatives are not known exactly. Numerical experiments are conducted to verify these theoretical rates. © 1996 John Wiley & Sons, Inc.