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Theory and Modern Applications

Table 3 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{100}\) and \(\alpha =0.3\) at \(T=1\) for Example 1

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

2.6920e-1

1.97

6.4002e-1

0.98

7.4278e-2

2.19

6.0812e-2

2.01

π/8

6.8944e-2

1.99

3.2373e-1

1.00

1.6283e-2

2.06

1.5082e-2

1.98

π/16

1.7324e-2

2.00

1.6238e-1

1.00

3.9158e-3

2.03

3.8272e-3

2.00

π/32

4.3295e-3

2.01

8.1255e-2

1.00

9.6026e-4

2.06

9.5437e-4

2.06

π/64

1.0753e-3

4.0636e-2

2.2993e-4

2.2955e-4