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Table 4
L1-norm of the coarse-fine differences of the pointwise densities ρ as a function of grid resolution for the linear acoustic wave test.
| Grid size | Fourth-order scheme | Second-order scheme | ||
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| coarse:fine | L1(Δρ) | Rate | L1(Δρ) | Rate |
|
|
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| 32:64 | 1.12E-09 | − | ||
| 64:128 | 4.80E-11 | 4.55 | ||
| 128:256 | 3.02E-12 | 3.99 | ||
| 256:512 | 1.89E-13 | 4.00 | ||
| 512:1024 | 1.20E-14 | 3.97 | ||
|
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| 322:642 | 6.26E-10 | − | 1.82E-09 | − |
| 642:1282 | 3.28E-11 | 4.26 | 4.39E-10 | 2.05 |
| 1282:2562 | 2.07E-12 | 3.99 | 1.10E-10 | 2.00 |
| 2562:5122 | 1.31E-13 | 3.98 | 2.74E-11 | 2.00 |
| 5122:10242 | 9.60E-15 | 3.77 | 6.85E-12 | 2.00 |
|
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| 323:643 | 3.95E-10 | − | 1.71E-09 | − |
| 643:1283 | 2.28E-11 | 4.11 | 4.31E-10 | 1.99 |
| 1283:2563 | 1.45E-12 | 3.97 | 1.09E-10 | 1.99 |
Notes. The corresponding convergence rates are also given.
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