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

Table 5

In 𝐺^𝑆, the minimum errors of the derivatives over the pairs (ℎ⁻¹,𝑛) in maximum norm when 𝜀=5×10⁻¹³.

(ℎ^−1,𝑛)	Max𝐺^𝑆𝑟^1/3𝜕𝑈^𝜀ℎ−𝜕𝑥𝜕𝑢𝜕𝑥	Max𝐺^𝑆𝑟^1/3𝜕𝑈^𝜀ℎ−𝜕𝑦𝜕𝑢𝜕𝑦
(16,70)	9.663×10^−6	9.663×10^−6
(32,170)	9.653×10^−6	9.653×10^−6
(64,170)	9.649×10^−6	9.649×10^−6
(128,200)	9.648×10^−6	9.648×10^−6