Analysis of the Block-Grid Method for the Solution of Laplace's Equation on Polygons with a Slit

Table 2

The errors by BGM when 9-point scheme is used with 𝑆⁶ interpolation.

(ℎ^−1,𝑛)	‖𝜀ℎ‖(𝐺^NS)	‖𝜀ℎ‖(𝐺^S)	‖𝜀ℎ^(1)‖(𝐺S)	‖𝜀ℎ^(2)‖(𝐺S)	iter.
(16, 100)	2.741×10^−9	4.895×10^−10	6.778×10^−10	2.293×10^−9	23
(16, 145)	2.789×10^−9	3.786×10^−10	5.108×10^−10	1.859×10^−9	23
(32, 100)	4.706×10^−11	7.158×10^−12	2.593×10^−10	4.691×10^−9	24
(32, 125)	4.805×10^−11	2.694×10^−12	6.623×10^−12	4.358×10^−11	24
(32, 130)	4.838×10^−11	1.831×10^−12	7.257×10^−12	5.186×10^−11	24
(32, 145)	4.745×10^−11	3.903×10^−12	8.808×10^−12	5.379×10^−11	24
(64, 125)	7.856×10^−13	2.220×10^−14	1.296×10^−12	3.364×10^−11	25
(64, 130)	7.545×10^−13	4.097×10^−14	5.376×10^−13	4.157×10^−11	25
(64, 145)	7.503×10^−13	4.396×10^−14	1.614×10^−13	1.312×10^−12	25