Table 2 Numerical results of the usual Galerkin FEM at \(t = 1\) (\(\tau =h^{2}\))
From: Low order nonconforming finite element method for time-dependent nonlinear Schrödinger equation
\(h=\frac{1}{16} \) | \(h=\frac{1}{32} \) | \(h=\frac{1}{64} \) | Ratio | |
|---|---|---|---|---|
\(\Vert {u}-{u}_{h}\Vert _{h} \) | 0.058940220 | 0.029468644 | 0.014523013 | 1.01 |
\(\Vert {u}-{u}_{h}\Vert _{0}\) | 0.001090311 | 0.000280127 | 0.000072122 | 1.96 |
\(\Vert \varPi _{h}u-u_{h}\Vert _{h}\) | 0.003725084 | 0.000970437 | 0.000253940 | 1.94 |
\(\Vert u-\varPi _{2h}u_{h}\Vert _{h}\) | 0.018165504 | 0.004580893 | 0.001067421 | 2.04 |
CPU time (s) | 68.88 | 5178.21 | 416,552.35 |