How to quantify Mesh Induced Errors in a Model (2nd Order Tet-Elements)

Hello to all simulation experts out there,

This question is not specifically related to a particular SIMULIA product but a recent observation in a support model.

I wanted to carry out a mesh independence study on a model in SOLIDWORKS Simulation. By keeping all the boundary conditions same, I started with a coarse mesh and gradually reduced the element size to reach a very fine level. 

I observed that the displacement values at a given location started to converge but for a particular element size, the values were totally out of the range (less than the expected result). Also the results were different, every time I re-run the study. At the first glance, I could not justify the results. 

One probable explanation would be that the elements were behaving abnormally "stiffer" than other cases. 

My question is:

Is there a method to quantitatively identify in a mesh, if at a certain location the elements are behaving stiffer?

Like by looking at a particular result value natively available in Software e.g. Energy Norm Error or Strain Energy or Strain Energy Density.

Thanks in advance for your expert opinions.

Regards