How to set up interior Neumann boundaries

Question

I'm solving the Poisson equation over subdomains with interior boundaries. I want to set up Neumann bcs on the interior boundaries. I followed the example in demo 22 "Poisson equation with multiple subdomains", replacing ds with dS:

boundaries = FacetFunction("size_t", mesh)
...
dSs = dS[boundaries]
...
L = f*v*dx + g*v*dSs(0)
...
b = assemble(L)

The last line gives the error message "Form argument must be restricted". How do I get this to work? (I've had no problems setting up Dirchlet bcs on internal boundaries.)

Answer 1

Hi, try

L = f*v*dx + g("+")*v("+")*dSs(0)

You can read about restrictions in the UFL manual. As long as g and v are not in DG spaces
you could equally restrict to the negative side, since both restrictions amount to the same DOF.

Comments

Thanks, that removed the error message, but the interior bc didn't take effect until I added the argument:

b = assemble(L, interior_facet_domains=boundary0)