Theory and Modern Applications
Table 2 Error results for Example 2 with mesh \((h,\tau)=(\frac{\sqrt{2}}{M},\frac{1}{M})\)
α | M | \(\|u-U\|_{L^{\infty}(L^{2}(\varOmega))}\) | Order | \(\| u-U\|_{L^{2}(H^{1}(\varOmega))}\) | Order |
|---|---|---|---|---|---|
0.01 | 10 | 3.73407198e-02 | – | 3.69550417e-01 | – |
20 | 9.23390100e-03 | 2.01573757 | 1.84671627e-01 | 1.00080897 | |
40 | 2.29539735e-03 | 2.00819635 | 9.22003887e-02 | 1.00211749 | |
80 | 5.72342061e-04 | 2.00379438 | 4.60524354e-02 | 1.00149538 | |
0.5 | 10 | 3.71756617e-02 | – | 3.69542982e-01 | – |
20 | 9.18108549e-03 | 2.01762178 | 1.84662989e-01 | 1.00084743 | |
40 | 2.28104835e-03 | 2.00896771 | 9.21960929e-02 | 1.00211723 | |
80 | 5.68639616e-04 | 2.00411051 | 4.60505161e-02 | 1.00148829 | |
0.99 | 10 | 3.69646868e-02 | – | 3.69533934e-01 | – |
20 | 9.11194883e-03 | 2.02031614 | 1.84651841e-01 | 1.00089921 | |
40 | 2.26187232e-03 | 2.01024215 | 9.21903788e-02 | 1.00211954 | |
80 | 5.63632504e-04 | 2.00469077 | 4.60479242e-02 | 1.00148007 |