Theory and Modern Applications
Table 5 Comparison of the \(L^{2}\) 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 | 5.97E−04 | – | 5.97E−04 | – | 7.81E−05 | – |
3 | 128 × 128 | 3.84E−05 | 3.96 | 3.84E−05 | 3.96 | 1.35E−06 | 5.85 |
4 | 256 × 256 | 2.41E−06 | 3.99 | 2.41E−06 | 3.99 | 2.17E−08 | 5.96 |
5 | 512 × 512 | 1.51E−07 | 4.00 | 1.51E−07 | 4.00 | 3.41E−10 | 5.99 |
6 | 1024 × 1024 | 9.45E−09 | 4.00 | 9.45E−09 | 4.00 | 6.27E−12 | 5.77 |