Table 6 Numerical results for \(\pmb{\mathbb{B}^{+}=[100,-200; -200,500]}\) , \(\pmb{\mathbb{B}^{-}=[1,-2; -2,5]}\)
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 | 1.0816 | - | 23.4214 | - |
16 × 16 | 3.9033E − 1 | 1.4704 | 16.6163 | 0.4952 | |
32 × 32 | 1.1628E − 1 | 1.7470 | 9.8040 | 0.7612 | |
64 × 64 | 3.1365E − 2 | 1.8904 | 5.3068 | 0.8855 | |
128 × 128 | 8.2005E − 3 | 1.9354 | 2.7690 | 0.9385 | |
256 × 256 | 2.0732E − 3 | 1.9839 | 1.4017 | 0.9822 | |
Incomplete PIFE (ε = 0) | 8 × 8 | 1.0751 | - | 23.1839 | - |
16 × 16 | 3.9068E − 1 | 1.4603 | 16.5401 | 0.4872 | |
32 × 32 | 1.1601E − 1 | 1.7518 | 9.7531 | 0.7620 | |
64 × 64 | 3.1393E − 2 | 1.8857 | 5.2968 | 0.8808 | |
128 × 128 | 8.2042E − 3 | 1.9360 | 2.7677 | 0.9364 | |
256 × 256 | 2.0726E − 3 | 1.9849 | 1.4011 | 0.9821 | |
Symmetric PIFE (ε = −1) | 8 × 8 | 1.0738 | - | 23.1231 | - |
16 × 16 | 3.9080E − 1 | 1.4582 | 16.5280 | 0.4844 | |
32 × 32 | 1.1596E − 1 | 1.7528 | 9.7468 | 0.7619 | |
64 × 64 | 3.1392E − 2 | 1.8852 | 5.2953 | 0.8802 | |
128 × 128 | 8.2055E − 3 | 1.9357 | 2.7674 | 0.9362 | |
256 × 256 | 2.0730E − 3 | 1.9848 | 1.4011 | 0.9820 |