Table 2 Comparing the errors with different types of norms and quasi-norms for Example 2 with \(p = 1.5\) and \(s = 0.6\) for SMRPI and EFG methods

\(|u-u_{h}|_{1,p}\)

EFG

7.135 × 10⁻³

3.352 × 10⁻³

1.612 × 10⁻³

7.856 × 10⁻⁴

3.908 × 10⁻⁴

SMRPI

3.321 × 10⁻¹

6.632 × 10⁻⁴

8.286 × 10⁻⁶

4.151 × 10⁻⁶

7.194 × 10⁻⁷

\(|u-u_{h}|_{u,p}\)

EFG

9.129 × 10⁻³

4.456 × 10⁻³

2.125 × 10⁻³

1.010 × 10⁻⁴

4.915 × 10⁻⁴

SMRPI

4.225 × 10⁻¹

2.025 × 10⁻⁴

7.887 × 10⁻⁶

9.301 × 10⁻⁷

1.811 × 10⁻⁷

\(|\sigma -\sigma _{h}|_{0,q}\)

EFG

1.094 × 10⁻²

6.371 × 10⁻³

3.518 × 10⁻³

1.825 × 10⁻⁴

9.108 × 10⁻⁴

SMRPI

4.521 × 10⁻¹

2.012 × 10⁻³

8.986 × 10⁻⁵

9.103 × 10⁻⁶

1.129 × 10⁻⁶

\(|\sigma -\sigma _{h}|_{\sigma ,q}\)

EFG

7.023 × 10⁻³

3.527 × 10⁻³

1.704 × 10⁻³

8.150 × 10⁻⁴

3.971 × 10⁻⁴

SMRPI

3.884 × 10⁻¹

1.938 × 10⁻³

6.416 × 10⁻⁵

5.553 × 10⁻⁶

1.112 × 10⁻⁶