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Theory and Modern Applications

Table 1 The semi-Lagrangian finite volume WENO 3 and WENO 5 methods on Example 1 with \(\pmb{t=5}\) , \(\pmb{\mathrm{CFL}=1.9}\)

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

9.04E − 04

-

1.41E − 03

-

1.58E − 04

-

2.46E − 04

-

40

1.41E − 04

2.68

2.22E − 04

2.67

5.05E − 06

4.97

7.92E − 06

4.96

80

1.64E − 05

3.10

2.58E − 05

3.11

1.58E − 07

5.00

2.49E − 07

4.99

160

2.09E − 06

2.97

3.29E − 06

2.97

5.31E − 09

4.90

8.35E − 09

4.90

320

2.62E − 07

2.99

4.11E − 07

3.00

1.63E − 10

5.03

2.05E − 10

5.06