I am trying to solve the heat equation for round heat sources and very 
small diffusion coefficients (<1e-7). Now when comparing the results 
between round heat sources and square heat sources, I get the following 
result for round heat sources: 
<https://lh3.googleusercontent.com/-6DAPX-JcWLg/Wnr49rTZxDI/AAAAAAAACcg/grQhq_phn1UIY9QMKirAuuVId0j2Hj0dgCLcBGAs/s1600/visit0002.png>



























and for square heat sources:


<https://lh3.googleusercontent.com/-TslXAsFzEoU/Wnr5TfQt1xI/AAAAAAAACck/Zjq9Vf7Qugk7LIZUem3bvetm82jGJfrIACLcBGAs/s1600/visit0001.png>


When comparing both results, I get spikes (i.e. overshooting values) at the 
border of the square heat source, but none at the border for the round heat 
source. I assume that there are discretization problems, after the 
problematic cells overlap with the grid cells. 


What can I do to minimize those spikes? They only appear for very low 
values of the diffusion coefficient, and get smaller for a higher grid 
resolution, but I can not remove them completely.


Thanks!





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