Table 7 Numerical results of u at \(t=2\)
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 |
|---|---|---|---|---|---|---|
16 × 16 | 6.6821 | / | 1.1840 | / | 1.2678 | / |
32 × 32 | 3.3145 | 1.0114 | 3.2218e−01 | 1.8778 | 3.3841e−01 | 1.9055 |
64 × 64 | 1.6538 | 1.0029 | 7.4794e−01 | 2.1068 | 7.5961e−02 | 2.1554 |
128 × 128 | 8.2649e−01 | 1.0007 | 1.5762e−02 | 2.2464 | 1.5813e−02 | 2.2641 |