Get isolines and create a new domain from them

I searched for “isolines” and “equipotential” but i didn’t find anything close to what I want. My problem is the following : i have an H¹ function u defined on a meshed domain. I would like to create a new domain {u > epsilon} and interpolate u on this new mesh to only work on it. Have you some hints on how to achieve that ?
Thank you for your help and have a great day !

Hello everyone,
I allow myself to up this thread since it doesn’t have any answer yet.
Have a nice day,

The problem you pose is very broad and somewhat difficult with many avenues of investigation. Furthermore your question is in the realm of mesh generation research rather than finite element discretisation. I doubt you’ll a quick answer from anyone here. Of course, I’d love to be proven wrong.

That’s understood, thank you. I will wait a few days more to see if anyone has an answer.
Have a good day.