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Theory and Modern Applications

Table 4 Order of convergence of Example 5.2

From: A fourth order block-hexagonal grid approximation for the solution of Laplace’s equation with singularities

\(\boldsymbol{2^{-m}}\)

\(\boldsymbol{2^{-5}}\)

\(\boldsymbol{2^{-6}}\)

\(\widetilde{R}_{P_{NS}^{1}}^{m}\)

16.257

15.9884

\(\widetilde{R}_{P_{NS}^{2}}^{m}\)

16.2387

16.0086

\(\widetilde{R}_{P_{S}^{1}}^{m}\)

19.3268

12.7771

\(\widetilde{R}_{P_{S}^{2}}^{m}\)

18.2604

14.0755