[firedrake] Internal dirichlet boundary conditions

[Thomas Ranner]

Hi,

I am interesting in solving elliptic problems where there is a 
Dirichlet condition on internal nodes. It seems like this isn't 
possible with the default DirichletBC class in firedrake - is that 
right and is there a nice work around?

My example is to do with remeshing and moving meshes. Consider the 
situation from 
https://www.firedrakeproject.org/demos/immersed_fem.py.html and 
suppose the want to recompute the mesh coordinates by solving

-Delta x = 0 in Omega_{1,2}
x = x_g on the interface and outside boundary

where x_g is the parametrisation on the interface which we want to 
be exactly given.

We have access to all the tags but this information doesn't change 
the solution. A couple of alternatives:
- use a Nitsche-type approach - this does ok but I would prefer to 
  not have this extra parameter unnecessarily.
- we can find the nodes which we are on the interface but I don't 
  know how to change the matrices/vectors to use this info.

Can you help?

Thanks,
Tom