Theory and Modern Applications
Table 1 Convergence order with respect to h of the stabilized method for Example 1 with \(P_{1}\) and \(P_{2}\) elements
From: A stabilized coupled method and its optimal error estimates for elliptic interface problems
\(\|\mathbf{u}-\mathbf{u}_{h}\|_{0}\) | Order (h) | \(\|\mathbf{u}-\mathbf{u}_{h}\|_{1}\) | Order (h) | |
|---|---|---|---|---|
h (\(P_{1}\)) | ||||
\(\frac{1}{16}\) | 1.04210e–1 | – | 2.70631 | – |
\(\frac{1}{32}\) | 2.68904e–2 | 1.954 | 1.36429 | 0.988 |
\(\frac{1}{64}\) | 6.79800e–3 | 1.984 | 0.683551 | 0.997 |
\(\frac{1}{128}\) | 1.70751e–3 | 1.993 | 0.341947 | 0.999 |
h (\(P_{2}\)) | ||||
\(\frac{1}{8}\) | 3.10623e–2 | – | 0.823449 | – |
\(\frac{1}{16}\) | 4.63642e–3 | 2.744 | 0.209248 | 1.976 |
\(\frac{1}{32}\) | 6.15439e–4 | 2.913 | 0.0522218 | 2.002 |
\(\frac{1}{64}\) | 7.83590e–5 | 2.973 | 0.0130404 | 2.002 |