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Theory and Modern Applications

Table 1 Error results for Example 1 with mesh \((h,\tau)=(\frac{\sqrt{2}}{M},\frac{1}{M})\)

From: Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations

α

M

\(\|u-U\|_{L^{\infty}(L^{2}(\varOmega))}\)

Order

\(\| u-U\|_{L^{2}(H^{1}(\varOmega))}\)

Order

0.01

10

4.68701563e-05

–

2.66537172e-02

–

20

1.17042557e-05

2.00163642

1.33031431e-02

1.00256959

40

2.90499824e-06

2.01042399

6.63449496e-03

1.00370860

80

7.22513815e-07

2.00744021

3.31169265e-03

1.00241786

0.5

10

4.68341426e-05

–

2.66488702e-02

–

20

1.16937976e-05

2.00181712

1.33003382e-02

1.00261144

40

2.90228354e-06

2.01048316

6.63303459e-03

1.00372197

80

7.21827421e-07

2.00746261

3.31095230e-03

1.00242282

0.99

10

4.67925509e-05

–

2.66432453e-02

–

20

1.16819417e-05

2.00199878

1.32971532e-02

1.00265242

40

2.89920905e-06

2.01054882

6.63137914e-03

1.00373656

80

7.21048696e-07

2.00749076

3.31011171e-03

1.00242903