Theory and Modern Applications
Table 2 Errors, estimators and effectivity ratio: \(\mathbf{P}_{1}-P_{1}\)
Meshes | Dof | \(\|\nabla \mathbf{e}\|_{0}\) | \(\|\epsilon \|_{0}\) | ⦀(e,ϵ)⦀ | η | \(\eta _{g}\) | \(E_{\eta }\) |
|---|---|---|---|---|---|---|---|
\(\mathcal{T}_{1}\) | 200 | 0.0775394 | 0.0357616 | 0.0853888 | 0.475923 | 0.0836507 | 5.5736 |
\(\mathcal{T}_{2}\) | 392 | 0.0554011 | 0.0212961 | 0.0593532 | 0.342517 | 0.0598029 | 5.7708 |
\(\mathcal{T}_{3}\) | 800 | 0.0387005 | 0.0122152 | 0.0405825 | 0.24037 | 0.0418828 | 5.9230 |
\(\mathcal{T}_{4}\) | 1800 | 0.0257246 | 0.00648786 | 0.0265301 | 0.160261 | 0.0279351 | 6.0407 |
\(\mathcal{T}_{5}\) | 3698 | 0.0179059 | 0.00370698 | 0.0182856 | 0.111726 | 0.0194876 | 6.1101 |
\(\mathcal{T}_{6}\) | 7200 | 0.0128105 | 0.00221413 | 0.0130004 | 0.080006 | 0.0139675 | 6.1541 |
\(\mathcal{T}_{7}\) | 14,450 | 0.00903022 | 0.00129542 | 0.00912266 | 0.0564323 | 0.00985919 | 6.1859 |