Theory and Modern Applications
Table 6 The \(L^{2}\) norm errors in time for case (d) 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 | 3.35E–04 | – | 9.46E–04 | – | 1.33E–03 | – |
32 | 1.69E–04 | 0.98 | 4.83E–04 | 0.97 | 6.83E–04 | 0.96 | |
64 | 8.51E–05 | 0.99 | 2.44E–04 | 0.98 | 3.46E–04 | 0.98 | |
128 | 4.27E–05 | 1.00 | 1.23E–04 | 0.99 | 1.74E–04 | 0.99 | |
SBD | 16 | 1.47E–05 | – | 4.88E–05 | – | 1.24E–04 | – |
32 | 3.63E–06 | 2.01 | 1.25E–05 | 1.97 | 3.29E–05 | 1.91 | |
64 | 9.02E–07 | 2.01 | 3.12E–06 | 2.00 | 8.40E–06 | 1.97 | |
128 | 2.25E–07 | 2.00 | 7.81E–07 | 2.00 | 2.12E–06 | 1.99 | |
L2-\(1_{\sigma }\) | 16 | 3.57E–04 | – | 1.73E–04 | – | 4.21E–05 | – |
32 | 1.67E–04 | 1.09 | 8.18E–05 | 1.08 | 1.27E–05 | 1.73 | |
64 | 8.04E–05 | 1.06 | 3.96E–05 | 1.05 | 4.80E–06 | 1.40 | |
128 | 3.92E–05 | 1.04 | 1.94E–05 | 1.03 | 2.20E–06 | 1.13 | |