Table 6 \(\pmb{L_{1}}\) and \(\pmb{L_{2}}\) errors analysis for the 2D Alfvén wave problem
2D circularly polarized Alfvén wave | ||||||
|---|---|---|---|---|---|---|
| Â | \(\boldsymbol{N}_{\boldsymbol{x}}\) | \(\boldsymbol{L}_{\boldsymbol{1}}\) error | \(\boldsymbol{L}_{\boldsymbol{1}}\) order | \(\boldsymbol{L}_{\boldsymbol{2}}\) error | \(\boldsymbol{L}_{\boldsymbol{2}}\) order | Theor. |
\(\mathbb{P}_{0}\mathbb{P}_{2}\) | 50 | 5.387E-02 | - | 9.527E-03 | - | 3 |
60 | 3.123E-02 | 2.99 | 5.523E-03 | 2.99 | ||
70 | 1.969E-02 | 2.99 | 3.481E-03 | 2.99 | ||
80 | 1.320E-02 | 2.99 | 2.334E-03 | 2.99 | ||
100 | 6.764E-03 | 3.00 | 1.196E-03 | 3.00 | ||
\(\mathbb{P}_{0}\mathbb{P}_{3}\) | 50 | 2.734E-04 | - | 4.888E-05 | - | 4 |
60 | 1.153E-04 | 4.73 | 2.061E-05 | 4.74 | ||
70 | 5.622E-05 | 4.66 | 1.004E-05 | 4.66 | ||
80 | 3.043E-05 | 4.60 | 5.422E-06 | 4.61 | ||
100 | 1.108E-05 | 4.53 | 1.968E-06 | 4.54 | ||
\(\mathbb{P}_{0}\mathbb{P}_{4}\) | 30 | 2.043E-03 | - | 3.611E-04 | - | 5 |
40 | 4.873E-04 | 4.98 | 8.615E-05 | 4.98 | ||
50 | 1.603E-04 | 4.98 | 2.846E-05 | 4.96 | ||
60 | 6.491E-05 | 4.96 | 1.168E-05 | 4.88 | ||
70 | 3.173E-05 | 4.64 | 6.147E-06 | 4.16 | ||