Table 3 The numerical results of the LDG method with the piecewise \(\pmb{P^{1}}\) space 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 | 0.0337 | - | 0.0057 | - |
20 | 0.0071 | 2.2469 | 7.9057e-04 | 2.8560 |
40 | 0.0018 | 2.0580 | 8.4326e-05 | 2.6283 |
80 | 4.6624e-04 | 1.9272 | 1.0537e-05 | 3.0005 |