Table 4 Numerical results of u at \(t=1.0\)
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 | 5.1679e−02 | / | 4.4691e−03 | / | 4.9353e−03 | / |
8 × 8 | 2.5582e−02 | 1.0144 | 1.1293e−03 | 1.9845 | 1.1598e−03 | 2.0891 |
16 × 16 | 1.2756e−02 | 1.0039 | 2.8497e−04 | 1.9865 | 2.8691e−04 | 2.0152 |
32 × 32 | 6.3737e−03 | 1.0010 | 7.2411e−05 | 1.9765 | 7.2534e−05 | 1.9838 |
64 × 64 | 3.1863e−03 | 1.0003 | 1.7824e−05 | 2.0201 | 1.7832e−05 | 2.0219 |