Theory and Modern Applications
Table 4 Comparison of the \(L^{\infty }\) errors and convergence order on different grid level of MG and EXFMG methods for Example 5.2
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 | 1.16E−02 | – | 1.16E−02 | – | 4.14E−01 | – |
3 | 128 × 128 | 5.36E−04 | 4.43 | 5.36E−04 | 4.43 | 2.01E−04 | 11.01 |
4 | 256 × 256 | 3.15E−05 | 4.09 | 3.15E−05 | 4.09 | 3.02E−06 | 6.06 |
5 | 512 × 512 | 1.94E−06 | 4.02 | 1.94E−06 | 4.02 | 6.18E−08 | 5.61 |
6 | 1024 × 1024 | 1.21E−07 | 4.01 | 1.21E−07 | 4.01 | 1.78E−09 | 5.12 |