Theory and Modern Applications
Table 4 Convergence order with respect to h of the stabilized method for Example 4 with coefficient functions
From: A stabilized coupled method and its optimal error estimates for elliptic interface problems
h | \(\|\mathbf{u}-\mathbf{u}_{h}\|_{0}\) | Order (h) | \(\|\mathbf{u}-\mathbf{u}_{h}\|_{1}\) | Order (h) | \(\|\mathbf{u}-\mathbf{u}_{h}\|_{0,\infty }\) | Order (h) | CPU (s) |
|---|---|---|---|---|---|---|---|
\(\frac{1}{16}\) | 4.39386e–3 | – | 3.84330e–2 | – | 8.04136e–3 | - | 0.725 |
\(\frac{1}{32}\) | 1.25230e–3 | 1.870 | 1.85753e–2 | 1.083 | 2.49653e–3 | 1.742 | 1.609 |
\(\frac{1}{64}\) | 2.30183e–4 | 2.441 | 8.35445e–3 | 1.151 | 5.91155e–4 | 2.076 | 7.721 |
\(\frac{1}{128}\) | 6.05530e–5 | 1.923 | 4.01170e–3 | 1.057 | 1.45916e–4 | 2.015 | 29.335 |
\(\frac{1}{256}\) | 1.48867e–5 | 2.008 | 1.95483e–3 | 1.029 | 3.48517e–5 | 2.050 | 99.845 |