Table 7 \(E^{N,M}_{\varepsilon ,\mu }\) and \(p^{N,M}_{\varepsilon ,\mu }\) with \(\mu =10^{-9}, \lambda =0, \) for Example 2
\(\varepsilon \downarrow \) | \( N=32 \) | \( N=64 \) | \( N=128 \) | \( N=256 \) |
|---|---|---|---|---|
\( \Delta t=0.25\) | \( \Delta t=0.25/2^{2}\) | \( \Delta t=0.25/2^{4} \) | \( \Delta t=0.25/2^{6} \) | |
\(10^{-0}\) | \( 2.8379e-04 \) | \( 9.3145e-05 \) | \( 2.4962e-05 \) | \( 6.3499e-06 \) |
1.6073 | 1.8997 | 1.9749 | ||
\(10^{-2}\) | \( 3.6086e-03 \) | \( 1.1504e-03 \) | \( 3.0489e-04 \) | \( 7.7337e-05 \) |
1.6493 | 1.9158 | 1.9791 | ||
\(10^{-4}\) | \( 4.5529e-03 \) | \( 1.4480e-03 \) | \( 3.8396e-04 \) | \( 9.7429e-05 \) |
1.6527 | 1.9150 | 1.9785 | ||
\(10^{-6}\) | \( 4.5651e-03 \) | \( 1.4523e-03 \) | \( 3.8509e-04 \) | \( 9.7695e-05 \) |
1.6523 | 1.9151 | 1.9788 | ||
\(10^{-8}\) | \( 4.5652e-03 \) | \( 1.4523e-03 \) | \( 3.8510e-04 \) | \( 9.7698e-05 \) |
1.6523 | 1.9150 | 1.9788 | ||
\(10^{-10}\) | \( 4.5652e-03 \) | \( 1.4523e-03 \) | \( 3.8510e-04 \) | \( 9.7698e-05 \) |
1.6523 | 1.9150 | 1.9788 | ||
\(10^{-12}\) | \( 4.5652e-03 \) | \( 1.4523e-03 \) | \( 3.8510e-04 \) | \( 9.7698e-05 \) |
1.6523 | 1.9150 | 1.9788 | ||
\(E_{\varepsilon ,\mu }^{N,M}\) | \( 4.5652e-03 \) | \( 1.4523e-03 \) | \( 3.8510e-04 \) | \( 9.7698e-05 \) |
Method in [35] | ||||
\(E_{\varepsilon ,\mu }^{N,M}\) | \( 1.1100e-02 \) | \( 2.4588e-03 \) | \( 6.0458e-04 \) | \( 1.5049e-04 \) |