New Properties of 9-Point Finite Difference Solution of the Laplace Equation

Two new properties of the 9-point finite difference solution of the Laplace equation are obtained, when the boundary functions are given from C 5,1 . It is shown that the maximum error is of order , and this order cannot be obtained for the class of boundary functions from C 5,λ , 0 < λ < 1. These properties of the 9-point solution can be used to justify different versions of domain decomposition, composite grids, and combined methods.