Table 5 The discrete \(L^{2}\) errors, maximum errors, and convergence rates for scheme (16) for Example 2 with \(v_{1}=0.1\) and \(v_{2}=0.9\)

π/4

1/4

1/10

2.3994e−2

3.0072e−2

π/8

1/16

1/20

1.5429e−3

3.9590

1.9337e−3

3.9590

π/16

1/64

1/40

9.6510e−5

3.9988

1.2096e−4

3.9988

π/32

1/256

1/80

6.0314e−6

4.0001

7.5593e−6

4.0001

π/64

1/1024

1/160

3.7695e−7

4.0000

4.7244e−7

4.0000

π/128

1/4096

1/320

2.3559e−8

4.0000

2.9527e−8

4.0000