Table 4 The numerical results of the LDG method with the piecewise \(\pmb{P^{2}}\) space at the final time \(\pmb{T=0.5}\)
N | \(\boldsymbol {e_{u}}\) | \(\boldsymbol{\xi_{u}}\) | ||
|---|---|---|---|---|
\(\boldsymbol{L^{2}}\) error | Order | \(\boldsymbol {L^{2}}\) error | Order | |
10 | 0.0018 | - | 6.5777e-04 | - |
20 | 1.9464e-04 | 2.9438 | 5.3149e-05 | 3.6295 |
40 | 2.3866e-05 | 3.0277 | 3.3170e-06 | 3.8606 |