Elements in overlap region between two different domains

Question

Hello
If we define two different domains with two different material properties, there are some elements in which are in both domains as shown below:

Two domains including inside and outside of the circle:

class Omega1(SubDomain):
  def inside(self, x, on_boundary):
   .
   .
   .
class Omega2(SubDomain):
  def inside(self, x, on_boundary):
   .
   .
   .
domains = CellFunction("size_t", mesh)

I want to know how FEniCS deals with this kind of situation because we have some elements with two different material properties that does not make sense. Could you please clarify it?
Thanks!

Answer 1

There are at least three ways:
1. live with the fact that the subdomain cuts elements. This would be default.
The subdomain is then defined in terms of the quadrature points inside and outside the subdomain. It can also be projected onto a polynomial space. But in any case it would be an approximation.
2. construct meshes that respect the subdomains (can be done in masher,
3. use sophisitcated cut-fem techniques that are being developed now (see e.g.
http://arxiv.org/abs/1505.00372)

Comments

That was a comprehensive response.
Thank you!

Answer 2

Hi,
You could consider re-meshing that respects the material boundary you want. Mshr lib. included in Fenics could help you.

Comments

Thanks for your response but it was like a very general comment.
I have written a code that works perfectly. So there should be some kind of approximation between the elements in the overlap region. I want to know how FEniCS handles it.
Does anyone have a better explanation by any chance?