Theory and Modern Applications
Table 1 Errors, estimators and effectivity ratio: \(\mathbf{P}_{1}-P_{0}\)
Meshes | Dof | \(\|\nabla \mathbf{e}\|_{0}\) | \(\|\epsilon \|_{0}\) | ⦀(e,ϵ)⦀ | η | \(\eta _{g}\) | \(E_{\eta }\) |
|---|---|---|---|---|---|---|---|
\(\mathcal{T}_{1}\) | 200 | 0.0781549 | 0.0827345 | 0.113812 | 0.48791 | 0.0836507 | 4.2870 |
\(\mathcal{T}_{2}\) | 392 | 0.0555608 | 0.0583028 | 0.0805371 | 0.360565 | 0.0598029 | 4.4770 |
\(\mathcal{T}_{3}\) | 800 | 0.0387081 | 0.0399877 | 0.0556537 | 0.257753 | 0.0418828 | 4.6314 |
\(\mathcal{T}_{4}\) | 1800 | 0.0257007 | 0.0260654 | 0.036605 | 0.174117 | 0.0279351 | 4.7566 |
\(\mathcal{T}_{5}\) | 3698 | 0.0178858 | 0.0178874 | 0.0252955 | 0.12227 | 0.0194876 | 4.8337 |
\(\mathcal{T}_{6}\) | 7200 | 0.0127973 | 0.0126668 | 0.0180061 | 0.0879465 | 0.0139675 | 4.8843 |
\(\mathcal{T}_{7}\) | 14,450 | 0.00902263 | 0.00885705 | 0.0126434 | 0.062228 | 0.00985919 | 4.9218 |