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Table 1 Results obtained for the slit problem

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

\(\boldsymbol{(h^{-1},n)}\) \(\boldsymbol{\Vert u-u_{h}\Vert _{\overline{D}_{NS}}}\) \(\boldsymbol{\Vert u-u_{h}\Vert _{\overline{D}_{S}}}\) \(\boldsymbol{R_{D_{NS}}^{m}}\) \(\boldsymbol{R_{D_{S}}^{m}}\)
(16,70) 5.924280 × 10−5 5.191270 × 10−7   
(32,70) 3.910378 × 10−6 4.794595 × 10−8 15.1501 10.8273
(64,110) 2.478126 × 10−7 2.558563 × 10−9 15.7796 18.7394
(128,130) 1.56560 × 10−8 1.27915 × 10−10 15.8286 20.0021