Theory and Modern Applications
Table 3 Comparison of the \(L^{\infty }\) errors and convergence order on different grid level of MG and EXFMG methods for Example 5.1
j | \(\Omega _{j}\) | MG | EXFMG | ||||
|---|---|---|---|---|---|---|---|
\(\Vert u-u_{j}^{*} \Vert _{\infty }\) | Order | \(\Vert u-\bar{u}^{*}_{j} \Vert _{\infty }\) | Order | \(\Vert u-u_{j}^{*} \Vert _{\infty }\) | Order | ||
2 | 64 × 64 | 1.56E−03 | – | 1.56E−03 | – | 3.44E−04 | – |
3 | 128 × 128 | 1.00E−04 | 3.96 | 1.00E−04 | 3.96 | 6.96E−06 | 5.63 |
4 | 256 × 256 | 6.30E−06 | 3.99 | 6.30E−06 | 3.99 | 1.23E−07 | 5.83 |
5 | 512 × 512 | 3.94E−07 | 4.00 | 3.94E−07 | 4.00 | 2.04E−09 | 5.91 |
6 | 1024 × 1024 | 2.47E−08 | 4.00 | 2.47E−08 | 4.00 | 7.10E−11 | 4.84 |