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

Table 1

The errors by BGM when 5-point scheme is used with 𝑆² interpolation.

(ℎ^−1,𝑛)	‖𝜀ℎ‖(𝐺^NS)	‖𝜀ℎ‖(𝐺^S)	‖𝜀ℎ^(1)‖(𝐺S)	‖𝜀ℎ^(2)‖(𝐺S)	iter
(16, 85)	6.138×10^−5	2.3127×10^−5	6.432×10^−5	4.464×10^−4	12
(16, 100)	5.264×10^−5	1.393×10^−5	5.126×10^−5	3.244×10^−4	12
(16, 120)	5.599×10^−5	1.150×10^−5	5.385×10^−5	3.430×10^−4	12
(32, 85)	1.317×10^−5	4.676×10^−6	1.129×10^−5	2.272×10^−5	13
(32, 100)	1.488×10^−5	1.889×10^−6	2.056×10^−5	1.523×10^−4	13
(32, 120)	1.491×10^−5	1.956×10^−6	2.053×10^−5	1.740×10^−4	13
(32, 130)	1.508×10^−5	5.172×10^−6	1.728×10^−5	4.659×10^−5	13
(32, 140)	1.571×10^−5	3.319×10^−6	2.407×10^−5	2.155×10^−4	13
(64, 130)	3.720×10^−6	7.391×10^−7	2.306×10^−6	1.941×10^−5	14
(64, 140)	3.583×10^−6	7.071×10^−7	3.852×10^−6	3.364×10^−5	14