Boundary Value Problems

Table 2 Approximation in a rectangle with less smooth exact solution

From: Approximation on the hexagonal grid of the Dirichlet problem for Laplace’s equation

h	${∥ ϵ_{h} ∥}_{Π^{h}}$	$R_{Π^{h}}^{m}$
2⁻³	1.9285677 × 10⁻⁴
2⁻⁴	1.1998304 × 10⁻⁵	16.0737
2⁻⁵	7.4809403 × 10⁻⁷	16.0385
2⁻⁶	4.67808169 × 10⁻⁸	15.9915
2⁻⁷	2.922653 × 10⁻⁹	16.0063

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