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Theory and Modern Applications

Table 4 The \(L^{2}\) norm errors in time for case (b) in Example 6.2 with \(h=1/10\)

From: Efficient Galerkin finite element methods for a time-fractional Cattaneo equation

Scheme

N

α = 1.1

α = 1.5

α = 1.9

\(L^{2}\) error

Rate

\(L^{2}\) error

Rate

\(L^{2}\) error

Rate

BE

16

8.96E–03

–

1.42E–02

–

2.84E–02

–

32

4.52E–03

0.99

7.50E–03

0.92

1.52E–02

0.90

64

2.27E–03

0.99

3.87E–03

0.96

7.87E–03

0.95

128

1.14E–03

1.00

1.97E–03

0.98

4.01E–03

0.97

SBD

16

5.75E–04

–

1.93E–03

–

2.91E–03

–

32

1.40E–04

2.04

4.63E–04

2.06

7.75E–04

1.91

64

3.46E–05

2.02

1.13E–04

2.04

1.98E–04

1.97

128

8.60E–06

2.01

2.77E–05

2.02

4.99E–05

1.99

L2-\(1_{\sigma }\)

16

7.78E–03

–

6.39E–03

–

1.88E–03

–

32

3.74E–03

1.06

2.92E–03

1.13

7.39E–04

1.35

64

1.83E–03

1.03

1.39E–03

1.07

3.23E–04

1.19

128

8.97E–04

1.03

6.78E–04

1.04

1.51E–04

1.10