I’m trying to calculate the correlation between the condition number of a finite elements matrix and the coarseness of the mesh that it represents.

However, when trying to calculate the Pearson correlation coefficient between the two, my data shows that at a very particular value of the parameter I use to quantify coarseness, the condition number of the matrix jumps up by quite a bit. I suspect this is due to the triangular elements of the matrix becoming very elongated, thus making the matrix ill-conditioned. However, there clearly is some sort of link between the two parameters, which doesn’t show up clearly when calculating the correlation.

My question is “How can I adjust the correlation calculation so as to still clearly indicate that there is such a link?”

To make all of this a bit clearer, here is a plot that shows what is going on quite well: