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Table 6 \(\pmb{L_{1}}\) and \(\pmb{L_{2}}\) errors analysis for the 2D Alfvén wave problem

From: Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

2D circularly polarized Alfvén wave
  \(\boldsymbol{N}_{\boldsymbol{x}}\) \(\boldsymbol{L}_{\boldsymbol{1}}\) 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
  1. The errors have been computed with respect to the magnetic field \(B^{y}\).