Boundary Value Problems

Table 1 Approximation in a rectangle with smooth exact solution

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

h	${∥ ϵ_{h} ∥}_{{\bar{Π}}^{h}}$	$R_{{\bar{Π}}^{h}}^{m}$
2⁻³	1.15727 × 10⁻⁷
2⁻⁴	7.33698 × 10⁻⁹	15.7731
2⁻⁵	4.58658 × 10⁻¹⁰	15.9966
2⁻⁶	2.89896 × 10⁻¹¹	15.4765
2⁻⁷	2.02482 × 10⁻¹²	14.3171

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