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 | 2.7798e-1 | 1.96 | 6.4097e-1 | 0.99 | 8.9179e-2 | 2.13 | 7.3655e-2 | 1.95 |
π/8 | 7.1673e-2 | 1.99 | 3.2382e-1 | 1.00 | 2.0417e-2 | 2.03 | 1.9064e-2 | 1.96 |
π/16 | 1.8050e-2 | 2.00 | 1.6239e-1 | 1.00 | 4.9828e-3 | 2.01 | 4.8843e-3 | 1.99 |
π/32 | 4.5193e-3 | 2.00 | 8.1256e-2 | 1.00 | 1.2363e-3 | 2.01 | 1.2298e-3 | 2.01 |
π/64 | 1.1288e-3 | ∗ | 4.0636e-2 | ∗ | 3.0656e-4 | ∗ | 3.0615e-4 | ∗ |