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Theory and Modern Applications

Table 2 The semi-Lagrangian finite volume WENO 3 and WENO 5 methods on Example 2 with \(\pmb{t=0.3}\) , \(\pmb{\mathrm{CFL}=2.9}\)

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

1.07E − 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