Skip to main content

Theory and Modern Applications

Table 1 Numerical results for Example  1 with \(\pmb{\tau=2^{-12}}\)

From: An expanded mixed finite element simulation for two-sided time-dependent fractional diffusion problem

β

h

1/16

1/32

1/64

1/128

Order

1/4

\(\Vert u-u_{h} \Vert \)

9.50e−03

4.78e−03

2.40e−03

1.20e−03

1.00

\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \)

3.33e−03

9.62e−04

2.81e−04

8.20e−05

1.78

\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \)

4.44e−03

1.43e−03

4.62e−04

1.50e−04

1.60

1/2

\(\Vert u-u_{h} \Vert \)

9.48e−03

4.77e−03

2.39e−03

1.20e−03

1.00

\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \)

1.43e−03

3.94e−04

1.07e−04

2.79e−05

1.92

\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \)

3.90e−03

1.15e−03

3.45e−04

1.05e−04

1.73

2/3

\(\Vert u-u_{h} \Vert \)

1.48e−02

7.53e−03

3.78e−03

1.89e−03

1.00

\(\vert\!\vert\!\vert p-p_{h}\vert\!\vert\!\vert \)

6.15e−04

1.69e−04

4.54e−05

1.19e−05

1.94

\(\vert\!\vert\!\vert q-q_{h}\vert\!\vert\!\vert \)

3.98e−03

1.09e−03

3.02e−04

8.37e−05

1.84