Theory and Modern Applications
Table 2 The \(L^{2}\) norm errors in space for Example 6.1 with \(N=4096\)
From: Efficient Galerkin finite element methods for a time-fractional Cattaneo equation
Scheme | 1/h | α = 1.1 | α = 1.5 | α = 1.9 | |||
|---|---|---|---|---|---|---|---|
\(L^{2}\) error | Rate | \(L^{2}\) error | Rate | \(L^{2}\) error | Rate | ||
BE | 4 | 1.35E–01 | – | 1.31E–01 | – | 1.20E–01 | – |
8 | 3.58E–02 | 1.92 | 3.46E–02 | 1.92 | 3.32E–02 | 1.85 | |
16 | 9.04E–03 | 1.98 | 8.74E–03 | 1.99 | 8.53E–03 | 1.96 | |
32 | 2.23E–03 | 2.02 | 2.14E–03 | 2.03 | 2.08E–03 | 2.04 | |
SBD | 4 | 1.35E–01 | – | 1.32E–01 | – | 1.20E–01 | – |
8 | 3.58E–02 | 1.92 | 3.47E–02 | 1.92 | 3.33E–02 | 1.84 | |
16 | 9.09E–03 | 1.98 | 8.80E–03 | 1.98 | 8.62E–03 | 1.95 | |
32 | 2.28E–03 | 1.99 | 2.21E–03 | 1.99 | 2.17E–03 | 1.99 | |
L2-\(1_{\sigma }\) | 4 | 1.35E–01 | – | 1.32E–01 | – | 1.20E–01 | – |
8 | 3.58E–02 | 1.92 | 3.47E–02 | 1.92 | 3.33E–02 | 1.84 | |
16 | 9.09E–03 | 1.98 | 8.80E–03 | 1.98 | 8.62E–03 | 1.95 | |
32 | 2.28E–03 | 1.99 | 2.21E–03 | 1.99 | 2.17E–03 | 1.99 | |