Theory and Modern Applications
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 | 1.07E − 03 | - | 3.40E − 03 | - | 1.15E − 04 | - | 5.22E − 04 | - |
40 | 1.30E − 04 | 3.04 | 4.47E − 04 | 2.93 | 4.05E − 06 | 4.83 | 2.08E − 05 | 4.65 |
80 | 1.60E − 05 | 3.02 | 5.84E − 05 | 2.94 | 1.27E − 07 | 5.00 | 7.21E − 07 | 4.85 |
160 | 1.98E − 06 | 3.01 | 7.19E − 06 | 3.02 | 3.96E − 09 | 5.00 | 2.31E − 08 | 4.96 |
200 | 1.01E − 06 | 3.02 | 3.67E − 06 | 3.01 | 1.30E − 09 | 4.99 | 7.58E − 09 | 4.99 |