Table 3 Numerical results of u at \(t=0.5\)
m × n | \(\|u^{n}-U^{n}_{h}\|_{1}\) | order | \(\|I_{h}u^{n}-U^{n}_{h}\|_{1}\) | order | \(\|u^{n}-I_{2h}U^{n}_{h}\|_{1}\) | order |
|---|---|---|---|---|---|---|
4 × 4 | 6.1063e−02 | / | 2.7140e−03 | / | 3.0059e−03 | / |
8 × 8 | 3.0096e−02 | 1.0207 | 6.7986e−04 | 1.9971 | 6.9905e−04 | 2.1043 |
16 × 16 | 1.4988e−02 | 1.0057 | 1.7159e−04 | 1.9862 | 1.7281e−04 | 2.0161 |
32 × 32 | 7.4865e−03 | 1.0014 | 4.3815e−05 | 1.9694 | 4.3893e−05 | 1.9771 |
64 × 64 | 3.7423e−03 | 1.0004 | 1.0696e−05 | 2.0338 | 1.0701e−05 | 2.0357 |