Table 6 The numerical results of the LDG method with the piecewise \(\pmb{P^{2}}\) 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 | 0.0016 | - | 4.2441e-04 | - |
20 | 1.9520e-04 | 3.0909 | 3.0008e-05 | 3.7303 |
40 | 2.5205e-05 | 2.9531 | 2.2068e-06 | 3.7653 |