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Table 7 Numerical results for \(\pmb{\mathbb{B}^{+}=[1,2; 2,5]}\) , \(\pmb{\mathbb{B}^{-}=[1\text{,}000,2\text{,}000; 2\text{,}000,5\text{,}000]}\)

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