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Theory and Modern Applications

Table 1 Numerical errors and convergence orders in temporal direction with \(h=\frac{\pi }{250}\) at \(T=1\) for Example 1

From: Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

α

τ

\(\|u^{n}-u_{h}^{n}\|_{1}\)

Rate

α = 1/3

1/2

4.4337e-2

1.97

1/4

1.1337e-2

2.00

1/8

2.8432e-3

2.01

1/16

7.0376e-4

2.07

1/32

1.6712e-4

α = 1/2

1/2

8.6340e-2

1.93

1/4

2.2736e-2

1.98

1/8

5.7464e-3

2.00

1/16

1.4383e-3

2.02

1/32

3.5459e-4

α = 2/3

1/2

1.4806e-1

1.87

1/4

4.0643e-2

1.97

1/8

1.0376e-2

1.99

1/16

2.6127e-3

2.00

1/32

6.5345e-4