Theory and Modern Applications
h | \(\|u^{n}-u_{h}^{n}\|\) | Rate | \(\|u^{n}-u_{h}^{n}\|_{1}\) | Rate | \(\|I_{h}u^{n}-u_{h}^{n}\|_{1}\) | Rate | \(\|u^{n}-\varPi _{2h}u_{h}^{n}\|_{1}\) | Rate |
---|---|---|---|---|---|---|---|---|
π/4 | 2.6920e-1 | 1.97 | 6.4002e-1 | 0.98 | 7.4278e-2 | 2.19 | 6.0812e-2 | 2.01 |
π/8 | 6.8944e-2 | 1.99 | 3.2373e-1 | 1.00 | 1.6283e-2 | 2.06 | 1.5082e-2 | 1.98 |
π/16 | 1.7324e-2 | 2.00 | 1.6238e-1 | 1.00 | 3.9158e-3 | 2.03 | 3.8272e-3 | 2.00 |
π/32 | 4.3295e-3 | 2.01 | 8.1255e-2 | 1.00 | 9.6026e-4 | 2.06 | 9.5437e-4 | 2.06 |
π/64 | 1.0753e-3 | ∗ | 4.0636e-2 | ∗ | 2.2993e-4 | ∗ | 2.2955e-4 | ∗ |