ABAQUS doc example: Contour integral evaluation: two-dimensional case

Hello, 

I am currently looking at an ABAQUS Doc example problem - ' Abaqus > Benchmarks > Analysis Tests > Fracture mechanics > Contour integral evaluation: two-dimensional case '. 

Please look at the 'Energy Release Rate' results (J-integral results) mentioned in Table 3. The 'G' values are fluctuating from 2.874 N/m to 2.485 N/m. 

This is clearly 'Domain dependency'. ABAQUS doc states 'Gradual variation in these estimates may indicate that a finer mesh is needed' and also states 'The J-integral should be path independent'. 

 

So, I am not sure why has DS included this example despite the domain dependency in the contour integral estimates. My question is that 

'Could this be a wrong example' or 'Do you mean to say that despite the fluctuations, this magnitude of fluctuations are normal and expected'?

Thanks in advance.

Best Regards,

Yu.