Table 6 \(E^{N,M}_{\varepsilon ,\mu }\) and \(p^{N,M}_{\varepsilon ,\mu }\) with \(\mu =10^{-3}, \lambda =0, \) for Example 1
\(\varepsilon \downarrow \) | \( N=32 \) | \( N=64 \) | \( N=128 \) | \( N=256 \) |
|---|---|---|---|---|
\( \Delta t=0.25\) | \( \Delta t=0.25/2^{2}\) | \( \Delta t=0.25/2^{4} \) | \( \Delta t=0.25/2^{6} \) | |
\(10^{-0}\) | \( 7.3970e-03 \) | \( 3.6490e-03 \) | \( 1.1642e-03 \) | \( 3.1262e-04 \) |
1.0194 | 1.6482 | 1.8969 | ||
\(10^{-2}\) | \( 1.9438e-02 \) | \( 5.4750e-03 \) | \( 1.4141e-03 \) | \( 3.5651e-04 \) |
1.8279 | 1.9530 | 1.9879 | ||
\(10^{-4}\) | \( 1.9861e-02 \) | \( 5.5330e-03 \) | \( 1.4235e-03 \) | \( 3.5849e-04 \) |
1.8438 | 1.9586 | Â | ||
\(10^{-6}\) | \( 1.9905e-02 \) | \( 5.5564e-03 \) | \( 1.4355e-03 \) | \( 3.6396e-04 \) |
1.8409 | 1.9526 | 1.9797 | ||
\(10^{-8}\) | \( 1.9905e-02 \) | \( 5.5564e-03 \) | \( 1.4355e-03 \) | \( 3.6459e-04 \) |
1.8409 | 1.9526 | 1.9772 | ||
\(10^{-10}\) | \( 1.9905e-02 \) | \( 5.5564e-03 \) | \( 1.4355e-03 \) | \( 3.6459e-04 \) |
1.8409 | 1.9526 | 1.9772 | ||
\(10^{-12}\) | \( 1.9905e-02 \) | \( 5.5564e-03 \) | \( 1.4355e-03 \) | \( 3.6459e-04 \) |
1.8409 | 1.9526 | 1.9772 | ||
\(E_{\varepsilon ,\mu }^{N,M}\) | \( 1.9905e-02 \) | \( 5.5564e-03 \) | \( 1.4355e-03 \) | \( 3.6459e-04 \) |
Method in [35] | ||||
\(E_{\varepsilon ,\mu }^{N,M}\) | \( 4.3706e-02 \) | \( 7.3807e-03 \) | \( 1.8967e-03 \) | \( 4.7927e-04 \) |