Table 2 Numerical results of u at \(t=0.1\)
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 | 7.2863e−02 | / | 6.4179e−04 | / | 7.1337e−04 | / |
8 × 8 | 3.5745e−02 | 1.0274 | 1.5938e−04 | 2.0095 | 1.6411e−04 | 2.1199 |
16 × 16 | 1.7779e−02 | 1.0075 | 4.0251e−05 | 1.9854 | 4.0554e−05 | 2.0168 |
32 × 32 | 8.8776e−03 | 1.0019 | 1.0329e−05 | 1.9622 | 1.0349e−05 | 1.9703 |
64 × 64 | 4.4373e−03 | 1.0005 | 2.4987e−06 | 2.0468 | 2.4999e−06 | 2.0489 |