From: A partially penalty immersed Crouzeix-Raviart finite element method for interface problems
Scheme | Grid | \(\boldsymbol{\|u-u_{h}\|_{0,\Omega }}\) | Order | \(\boldsymbol{|u-u_{h}|_{1,h}}\) | Order |
---|---|---|---|---|---|
Nonsymmetric PIFE (ε = 1) | 8 × 8 | 1.2074E − 1 | - | 2.3185 | - |
16 × 16 | 3.1092E − 2 | 1.9573 | 1.1779 | 0.9769 | |
32 × 32 | 7.8627E − 3 | 1.9835 | 5.9427E − 1 | 0.9871 | |
64 × 64 | 1.9738E − 3 | 1.9940 | 2.9834E − 1 | 0.9942 | |
128 × 128 | 4.9306E − 4 | 2.0011 | 1.4939E − 1 | 0.9979 | |
256 × 256 | 1.2335E − 4 | 1.9991 | 7.4748E − 2 | 0.9990 | |
Incomplete PIFE (ε = 0) | 8 × 8 | 1.1978E − 1 | - | 2.3039 | - |
16 × 16 | 3.1017E − 2 | 1.9492 | 1.1766 | 0.9695 | |
32 × 32 | 7.8636E − 3 | 1.9798 | 5.9412E − 1 | 0.9858 | |
64 × 64 | 1.9749E − 3 | 1.9934 | 2.9833E − 1 | 0.9939 | |
128 × 128 | 4.9317E − 4 | 2.0016 | 1.4936E − 1 | 0.9981 | |
256 × 256 | 1.2339E − 4 | 1.9989 | 7.4745E − 2 | 0.9987 | |
Symmetric PIFE (ε = −1) | 8 × 8 | 1.1967E − 1 | - | 2.3025 | - |
16 × 16 | 3.1010E − 2 | 1.9482 | 1.1765 | 0.9687 | |
32 × 32 | 7.8665E − 3 | 1.9790 | 5.9412E − 1 | 0.9857 | |
64 × 64 | 1.9752E − 3 | 1.9937 | 2.9833E − 1 | 0.9938 | |
128 × 128 | 4.9317E − 4 | 2.0018 | 1.4936E − 1 | 0.9981 | |
256 × 256 | 1.2337E − 4 | 1.9991 | 7.4745E − 2 | 0.9987 |