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Theory and Modern Applications

Table 5 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\), \(\beta =2\) and \(\alpha =0.1\) at \(T=1\) for Example 2

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

h

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

Rate

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

Rate

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

Rate

\(\|u^{n}-\varPi _{2h}u_{h}^{n}\|_{1}\)

Rate

π/4

2.7798e-1

1.96

6.4097e-1

0.99

8.9179e-2

2.13

7.3655e-2

1.95

π/8

7.1673e-2

1.99

3.2382e-1

1.00

2.0417e-2

2.03

1.9064e-2

1.96

π/16

1.8050e-2

2.00

1.6239e-1

1.00

4.9828e-3

2.01

4.8843e-3

1.99

π/32

4.5193e-3

2.00

8.1256e-2

1.00

1.2363e-3

2.01

1.2298e-3

2.01

π/64

1.1288e-3

4.0636e-2

3.0656e-4

3.0615e-4