**Edited:  Changed after studying solution** 

Plotting sol[x,y,8] below one sees it begins very small oscillations  between positive and negative values assuming the machine-precision FEM method employed yields and accurate solution and the oscillations aren't spurious.  One could back-substitue the solution to check this.  Assuming the solution is indeed correct, then this is  of course problematic if one is interested in taking the log of the solution unless further processing of the solution is acceptable such as using absolute values or other methods.  

[![enter image description here][1]][1]


[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/jdiXW.jpg
  [2]: https://i.sstatic.net/fsRxd.jpg