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 | 4.9337E − 3 | - | 8.0908E − 2 | - |
16 × 16 | 1.1162E − 3 | 2.1441 | 4.3830E − 2 | 0.8844 | |
32 × 32 | 2.9009E − 4 | 1.9440 | 2.2917E − 2 | 0.9355 | |
64 × 64 | 6.5676E − 5 | 2.1431 | 1.1502E − 2 | 0.9946 | |
128 × 128 | 1.8919E − 5 | 1.7955 | 5.7744E − 3 | 0.9941 | |
256 × 256 | 4.4585E − 6 | 2.0852 | 2.8965E − 3 | 0.9954 | |
Incomplete PIFE (ε = 0) | 8 × 8 | 5.5911E − 3 | - | 8.1187E − 2 | - |
16 × 16 | 1.3044E − 3 | 2.0997 | 4.4172E − 2 | 0.6087 | |
32 × 32 | 3.2578E − 4 | 2.0014 | 2.3182E − 2 | 0.9301 | |
64 × 64 | 6.9110E − 5 | 2.2369 | 1.1552E − 2 | 1.0048 | |
128 × 128 | 1.8967E − 5 | 1.8654 | 5.7761E − 3 | 1.0000 | |
256 × 256 | 4.4796E − 6 | 2.0820 | 2.8974E − 3 | 0.9953 | |
Symmetric PIFE (ε = −1) | 8 × 8 | 6.0212E − 3 | - | 8.1462E − 2 | - |
16 × 16 | 1.3636E − 3 | 2.1426 | 4.4097E − 2 | 0.8854 | |
32 × 32 | 3.3744E − 4 | 2.0147 | 2.3284E − 2 | 0.9214 | |
64 × 64 | 7.1179E − 5 | 2.2451 | 1.1612E − 2 | 1.0037 | |
128 × 128 | 1.8993E − 5 | 1.9060 | 5.7769E − 3 | 1.0073 | |
256 × 256 | 4.4914E − 6 | 2.0802 | 2.8981E − 3 | 0.9952 |