Skip to main content

Table 2 Numerical results for \(\pmb{(\beta^{-},\beta^{+})=(1\text{,}000,1)}\) with different PIFE schemes

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