Theory and Modern Applications
Table 7 The \(L^{2}\) norm errors in time for case (e) 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 | 2.38E–04 | – | 1.47E–04 | – | 1.50E–04 | – |
32 | 1.21E–04 | 0.98 | 7.55E–05 | 0.97 | 7.66E–05 | 0.97 | |
64 | 6.07E–05 | 0.99 | 3.82E–05 | 0.98 | 3.87E–05 | 0.98 | |
128 | 3.05E–05 | 1.00 | 1.92E–05 | 0.99 | 1.94E–05 | 0.99 | |
SBD | 16 | 9.34E–06 | – | 1.22E–05 | – | 6.45E–06 | – |
32 | 2.33E–06 | 2.00 | 3.02E–06 | 2.02 | 1.66E–06 | 1.96 | |
64 | 5.81E–07 | 2.00 | 7.48E–07 | 2.01 | 4.18E–07 | 1.99 | |
128 | 1.45E–07 | 2.00 | 1.86E–07 | 2.01 | 1.05E–07 | 2.00 | |
L2-\(1_{\sigma }\) | 16 | 3.38E–04 | – | 1.74E–04 | – | 1.95E–05 | – |
32 | 1.63E–04 | 1.06 | 8.23E–05 | 1.08 | 9.25E–06 | 1.07 | |
64 | 7.93E–05 | 1.04 | 3.98E–05 | 1.05 | 4.50E–06 | 1.04 | |
128 | 3.89E–05 | 1.03 | 1.94E–05 | 1.03 | 2.22E–06 | 1.02 | |