Theory and Modern Applications
Table 1 The \(L^{2}\) norm errors in time for Example 6.1 with \(h=1/512\)
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 | 4 | 4.55E–02 | – | 6.43E–02 | – | 9.01E–02 | – |
8 | 2.43E–02 | 0.91 | 3.46E–02 | 0.89 | 4.96E–02 | 0.86 | |
16 | 1.25E–02 | 0.95 | 1.80E–02 | 0.95 | 2.62E–02 | 0.92 | |
32 | 6.37E–03 | 0.98 | 9.16E–03 | 0.97 | 1.35E–02 | 0.96 | |
SBD | 4 | 1.25E–02 | – | 1.65E–02 | – | 2.17E–02 | – |
8 | 3.31E–03 | 1.92 | 4.08E–03 | 2.02 | 4.53E–03 | 2.26 | |
16 | 8.41E–04 | 1.98 | 9.99E–04 | 2.03 | 8.78E–04 | 2.37 | |
32 | 2.07E–04 | 2.02 | 2.44E–04 | 2.03 | 1.86E–04 | 2.24 | |
L2-\(1_{\sigma }\) | 4 | 5.83E–03 | – | 1.38E–02 | – | 2.81E–02 | – |
8 | 1.50E–03 | 1.96 | 3.77E–03 | 1.87 | 7.40E–03 | 1.93 | |
16 | 3.75E–04 | 2.00 | 9.75E–04 | 1.95 | 1.88E–03 | 1.98 | |
32 | 8.86E–05 | 2.08 | 2.52E–04 | 1.95 | 4.77E–04 | 1.98 | |