Table 2 The numerical errors
Basis | h | α | \(\|u-u_{h}\|_{\infty}\) | \(\|u-u_{h}\|_{0}\) | \(|u-u_{h}|_{1}\) |
|---|---|---|---|---|---|
Lagrange | \(\frac{1}{4} \) | – | 3.4000e − 03 | 1.9000e − 03 | 5.0900e − 02 |
\(\frac{1}{8} \) | – | 4.1488e − 04 | 2.4555e − 04 | 1.2800e − 02 | |
\(\frac{1}{16} \) | – | 4.9912e − 05 | 3.0760e − 05 | 3.2000e − 03 | |
\(\frac{1}{32} \) | – | 6.0911e − 06 | 3.8470e − 06 | 7.9789e − 04 | |
[3pt] C-Bézier | \(\frac{1}{4} \) | \(\frac{\pi}{4}\) | 1.3192e − 08 | 7.4480e − 09 | 2.0785e − 07 |
\(\frac{1}{8} \) | \(\frac{\pi}{8}\) | 4.9641e − 11 | 2.6246e − 11 | 1.5837e − 09 | |
\(\frac{1}{16} \) | \(\frac{\pi}{16}\) | 7.5162e − 14 | 4.0419e − 14 | 4.9740e − 12 | |
\(\frac{1}{32} \) | \(\frac{\pi}{32}\) | 6.8501e − 14 | 3.1989e − 14 | 3.6248e − 12 |