Table 1 Numerical results of two-grid Algorithm 4.1 at \(t = 1\) (\(\tau =h^{2}\), \(h\approx H^{2}\))
From: Low order nonconforming finite element method for time-dependent nonlinear Schrödinger equation
\(h=\frac{1}{16}\), \(H=\frac{1}{4} \) | \(h=\frac{1}{32}\), \(H=\frac{1}{6} \) | \(h=\frac{1}{64}\), \(H=\frac{1}{8} \) | Ratio | |
|---|---|---|---|---|
\(\Vert {u}-{u}_{h}\Vert _{h} \) | 0.058942538 | 0.029468965 | 0.014736033 | 0.99 |
\(\Vert {u}-{u}_{h}\Vert _{0}\) | 0.001096657 | 0.000281836 | 0.000075823 | 1.93 |
\(\Vert \varPi _{h}u-u_{h}\Vert _{h}\) | 0.003761590 | 0.000980134 | 0.000264975 | 1.91 |
\(\Vert u-\varPi _{2h}u_{h}\Vert _{h}\) | 0.018173033 | 0.004582958 | 0.001179143 | 1.97 |
CPU time (s) | 54.06 | 2973.62 | 237,992.52 |