A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in 𝐶^𝑘,𝜆

Table 3

The minimum errors of the solution over the pairs (ℎ⁻¹,𝑛) in maximum norm when 𝜀=5×10⁻¹³.

(ℎ^−1,𝑛)	‖𝜁^𝜀ℎ‖𝐺^𝑁𝑆	‖𝜁^𝜀ℎ‖𝐺^𝑆	Iteration
(16,70)	1.139×10^−8	1.572×10^−8	22
(32,170)	1.033×10^−9	1.184×10^−9	23
(64,170)	6.990×10^−11	7.304×10^−11	24
(128,200)	8.628×10^−12	8.833×10^−12	25