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

Table 1

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

(2^−𝜚,𝑛)	‖𝜁^𝜀ℎ‖𝐺^𝑁𝑆	ℜ^𝜚𝐺𝑁𝑆
(2^−4,60)	1.609×10^−8	15.577
(2^−5,170)	1.033×10^−9
(2^−5,130)	1.191×10^−9	16.690
(2^−6,150)	7.136×10^−11
(2^−5,140)	1.136×10^−9	16.259
(2^−6,170)	6.991×10^−11
(2^−6,100)	2.169×10^−10	17.096
(2^−7,130)	1.269×10^−11