Table 5 The numerical results of the LDG method with the piecewise \(\pmb{P^{1}}\) at the final time \(\pmb{T=1}\)
N | \(\boldsymbol {e_{u}}\) | \(\boldsymbol{\xi_{u}}\) | ||
|---|---|---|---|---|
\(\boldsymbol{L^{2}}\) error | Order | \(\boldsymbol {L^{2}}\) error | Order | |
10 | 0.0252 | - | 0.0031 | - |
20 | 0.0072 | 1.8027 | 4.3012e-04 | 2.8375 |
40 | 0.0018 | 2.0197 | 5.2154e-05 | 3.2029 |
80 | 4.4483e-04 | 2.0049 | 7.0841e-06 | 2.8801 |