Theory and Modern Applications
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 | 8.96E–03 | – | 1.42E–02 | – | 2.84E–02 | – |
32 | 4.52E–03 | 0.99 | 7.50E–03 | 0.92 | 1.52E–02 | 0.90 | |
64 | 2.27E–03 | 0.99 | 3.87E–03 | 0.96 | 7.87E–03 | 0.95 | |
128 | 1.14E–03 | 1.00 | 1.97E–03 | 0.98 | 4.01E–03 | 0.97 | |
SBD | 16 | 5.75E–04 | – | 1.93E–03 | – | 2.91E–03 | – |
32 | 1.40E–04 | 2.04 | 4.63E–04 | 2.06 | 7.75E–04 | 1.91 | |
64 | 3.46E–05 | 2.02 | 1.13E–04 | 2.04 | 1.98E–04 | 1.97 | |
128 | 8.60E–06 | 2.01 | 2.77E–05 | 2.02 | 4.99E–05 | 1.99 | |
L2-\(1_{\sigma }\) | 16 | 7.78E–03 | – | 6.39E–03 | – | 1.88E–03 | – |
32 | 3.74E–03 | 1.06 | 2.92E–03 | 1.13 | 7.39E–04 | 1.35 | |
64 | 1.83E–03 | 1.03 | 1.39E–03 | 1.07 | 3.23E–04 | 1.19 | |
128 | 8.97E–04 | 1.03 | 6.78E–04 | 1.04 | 1.51E–04 | 1.10 |