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

Table 2

The order of convergence in the “singular” part when ℎ=2^−𝜚 and 𝜀=5×10⁻¹³.

(2^−𝜚,𝑛)	‖𝜁^𝜀ℎ‖𝐺^𝑆	ℜ^𝜚𝐺𝑆
(2^−4,100)	1.931×10^−8	16.078
(2^−5,150)	1.182×10^−9
(2^−5,130)	1.294×10^−9	16.789
(2^−6,150)	7.708×10^−11
(2^−5,140)	1.312×10^−9	17.967
(2^−6,170)	7.304×10^−11
(2^−6,100)	2.389×10^−10	18.164
(2^−7,130)	1.315×10^−11