Theory and Modern Applications
Table 1 Accuracy test for equation ( 5.1 )
From: A discontinuous Galerkin finite element method for the Zakharov-Kuznetsov equation
|  | N  ×  N | \(\boldsymbol{L^{2}}\) -error | Order | \(\boldsymbol{L^{1}}\) -error | Order |
|---|---|---|---|---|---|
\(Q^{2}\) | 20 × 20 | 3.032018840302996E-004 | - | 2.779219730679066E-003 | - |
30 × 30 | 9.038730179467316E-005 | 2.98 | 7.946304825147322E-004 | 3.09 | |
40 × 40 | 3.841265719078744E-005 | 2.97 | 3.349696193814798E-004 | 3.00 | |
50 × 50 | 1.986670810126657E-005 | 2.95 | 1.738770541364282E-004 | 2.94 | |
\(Q^{3}\) | 20 × 20 | 2.722203359313328E-005 | - | 2.741631230523309E-004 | - |
30 × 30 | 5.748716715063882E-006 | 3.84 | 5.293369829707573E-005 | 4.06 | |
40 × 40 | 1.907211474086055E-006 | 3.84 | 1.725162974740285E-005 | 3.90 | |
50 × 50 | 8.897496837295630E-007 | 3.42 | 7.876941867550543E-006 | 3.51 |