Theory and Modern Applications
Table 5 The \(L^{2}\) norm errors in time for case (c) 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 | 2.36E–05 | – | 4.38E–05 | – | 3.40E–05 | – |
32 | 1.20E–05 | 0.98 | 2.21E–05 | 0.99 | 1.69E–05 | 1.01 | |
64 | 6.02E–06 | 0.99 | 1.11E–05 | 0.99 | 8.45E–06 | 1.00 | |
128 | 3.02E–06 | 1.00 | 5.55E–06 | 1.00 | 4.22E–06 | 1.00 | |
SBD | 16 | 1.65E–07 | – | 8.88E–07 | – | 1.55E–06 | – |
32 | 4.81E–08 | 1.78 | 2.15E–07 | 2.05 | 3.92E–07 | 1.98 | |
64 | 1.28E–08 | 1.91 | 5.27E–08 | 2.03 | 9.85E–08 | 1.99 | |
128 | 3.30E–09 | 1.96 | 1.30E–08 | 2.01 | 2.47E–08 | 2.00 | |
L2-\(1_{\sigma }\) | 16 | 2.80E–05 | – | 1.13E–05 | – | 7.59E–07 | – |
32 | 1.32E–05 | 1.08 | 5.53E–06 | 1.03 | 4.39E–07 | 0.79 | |
64 | 6.40E–06 | 1.05 | 2.71E–06 | 1.03 | 2.35E–07 | 0.90 | |
128 | 3.13E–06 | 1.03 | 1.34E–06 | 1.02 | 1.21E–07 | 0.95 | |