Skip to main content

Theory and Modern Applications

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