Theory and Modern Applications
Table 6 Comparison of the \(L^{2}\) 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 | 1.37E−03 | – | 1.37E−03 | – | 1.59E−01 | – |
3 | 128 × 128 | 5.85E−05 | 4.55 | 5.85E−05 | 4.55 | 2.23E−05 | 12.80 |
4 | 256 × 256 | 3.46E−06 | 4.08 | 3.46E−06 | 4.08 | 2.84E−07 | 6.29 |
5 | 512 × 512 | 2.13E−07 | 4.02 | 2.13E−07 | 4.02 | 4.40E−09 | 6.01 |
6 | 1024 × 1024 | 1.33E−08 | 4.00 | 1.33E−08 | 4.00 | 3.38E−10 | 3.70 |