Theory and Modern Applications
Table 3 The \(L^{2}\) norm errors in time for case (a) 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 | 3.43E–04 | – | 8.09E–05 | – | 1.79E–04 | – |
32 | 1.74E–04 | 0.98 | 4.18E–05 | 0.95 | 9.11E–05 | 0.98 | |
64 | 8.74E–05 | 0.99 | 2.13E–05 | 0.97 | 4.59E–05 | 0.99 | |
128 | 4.39E–05 | 1.00 | 1.07E–05 | 0.99 | 2.30E–05 | 0.99 | |
SBD | 16 | 3.53E–06 | – | 1.25E–05 | – | 5.30E–06 | – |
32 | 7.64E–07 | 2.21 | 3.16E–06 | 1.99 | 1.38E–06 | 1.94 | |
64 | 1.78E–07 | 2.10 | 7.90E–07 | 2.00 | 3.52E–07 | 1.98 | |
128 | 4.32E–08 | 2.05 | 1.98E–07 | 2.00 | 8.86E–08 | 1.99 | |
L2-\(1_{\sigma }\) | 16 | 5.46E–04 | – | 2.42E–04 | – | 2.25E–05 | – |
32 | 2.63E–04 | 1.06 | 1.15E–04 | 1.07 | 1.08E–05 | 1.05 | |
64 | 1.28E–04 | 1.04 | 5.58E–05 | 1.05 | 5.32E–06 | 1.03 | |
128 | 6.29E–05 | 1.03 | 2.73E–05 | 1.03 | 2.63E–06 | 1.01 | |