Theory and Modern Applications
Table 3 The semi-Lagrangian finite volume WENO 3 and WENO 5 methods on Example 3 with \(\pmb{t=2}\) , \(\pmb{\mathrm{CFL}=9.9}\)
From: Higher-order finite volume method with semi-Lagrangian scheme for one-dimensional conservation laws
N | SL-FV 3 | SL-FV 5 | ||||||
|---|---|---|---|---|---|---|---|---|
\(\boldsymbol{L^{1}}\) error | Order | \(\boldsymbol{L^{\infty}}\) error | Order | \(\boldsymbol{L^{1}}\) error | Order | \(\boldsymbol{L^{\infty}}\) error | Order | |
20 | 1.91E − 03 | - | 2.99E − 03 | - | 4.01E − 05 | - | 6.22E − 05 | - |
40 | 2.54E − 04 | 2.91 | 3.98E − 04 | 2.91 | 1.27E − 06 | 4.98 | 1.99E − 06 | 4.97 |
80 | 3.22E − 05 | 2.98 | 5.05E − 05 | 2.98 | 4.10E − 08 | 4.95 | 6.15E − 08 | 5.02 |
160 | 4.03E − 06 | 3.00 | 6.33E − 06 | 3.00 | 1.29E − 09 | 4.99 | 1.84E − 09 | 5.06 |
200 | 2.07E − 06 | 2.99 | 3.24E − 06 | 3.00 | 4.24E − 10 | 4.99 | 5.73E − 10 | 5.23 |