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 | 1.0678E − 2 | - | 4.7925E − 1 | - |
16 × 16 | 2.4087E − 3 | 2.1483 | 2.3967E − 1 | 0.9997 | |
32 × 32 | 5.7775E − 4 | 2.0597 | 1.1989E − 1 | 0.9993 | |
64 × 64 | 1.4172E − 4 | 2.0274 | 5.9947E − 2 | 1.0000 | |
128 × 128 | 3.5894E − 5 | 1.9812 | 2.9981E − 2 | 0.9996 | |
256 × 256 | 8.8877E − 6 | 2.0139 | 1.4993E − 2 | 0.9998 | |
Incomplete PIFE (ε = 0) | 8 × 8 | 1.0510E − 2 | - | 4.7886E − 1 | - |
16 × 16 | 2.3468E − 3 | 2.1630 | 2.3937E − 1 | 1.0004 | |
32 × 32 | 5.7093E − 4 | 2.0393 | 1.1983E − 1 | 0.9982 | |
64 × 64 | 1.4131E − 4 | 2.0144 | 5.9947E − 2 | 0.9992 | |
128 × 128 | 3.5885E − 5 | 1.9775 | 2.9982E − 2 | 0.9996 | |
256 × 256 | 8.8873E − 6 | 2.0136 | 1.4993E − 2 | 0.9998 | |
Symmetric PIFE (ε = −1) | 8 × 8 | 1.0501E − 2 | - | 4.7883E − 1 | - |
16 × 16 | 2.3443E − 3 | 2.1633 | 2.3935E − 1 | 1.0004 | |
32 × 32 | 5.7071E − 4 | 2.0383 | 1.1984E − 1 | 0.9981 | |
64 × 64 | 1.4128E − 4 | 2.0142 | 5.9948E − 2 | 0.9993 | |
128 × 128 | 3.5883E − 5 | 1.9772 | 2.9983E − 2 | 0.9996 | |
256 × 256 | 8.8910E − 6 | 2.0129 | 1.4993E − 2 | 0.9998 |