Table 4 The discrete \(L^{2}\) errors, maximum errors, and their convergence rates for scheme (8) for Example 2 when \(v_{1}=0.1\) and \(v_{2}=0.9\)

π/4

1/8

1/10

3.2542e−2

4.0785e−2

π/8

1/16

1/20

8.0780e−3

2.0102

1.0124e−2

2.0102

π/16

1/32

1/40

2.0157e−3

2.0027

2.5263e−3

2.0027

π/32

1/64

1/80

5.0368e−4

2.0007

6.3126e−4

2.0007

π/64

1/128

1/160

1.2590e−4

2.0002

1.5780e−4

2.0002

π/128

1/256

1/320

3.1475e−5

2.0000

3.9448e−5

2.0000

π/256

1/512

1/640

7.8687e−6

2.0000

9.8619e−6

2.0000

π/512

1/1024

1/1280

1.9672e−6

2.0000

2.4655e−6

2.0000