I would like to solve a problem involving three 1D domains connected with a T joint at coordinates (0,0):
Domain 1 is a line between (-1,0) and (0,0) where f1 is solve.
Domain 2 is a line between (0,0) and (1,0) where f2 is solve,
Domain 3 is a line between (0,0) and (0,1) where f3 is solve.
The equations on f1, f2 and f3 are not the same of the three domains. A condition is imposed on f1, f2 and f3 at the joint (0,0), for instance f1+f2+f3=0. My idea is to solve this by means of the DG method. For instance on the domain 1, I would like to impose a flux between f1 and an exterior trace defined as -f2-f3 on the boundary at (0,0). But is there a way to do something like that? Can I access the boundary values of f2 and f3 in a form written on domain 1?
Thank you for your answer! It looks like what I want to do. I will dive into the problem more in details but if I understand correctly the big lines, I’ll have to create a 2D mesh that has edges (at the boundary or internal) that match exactly the three 1D domains?
If your mesh is a 1D mesh, I would make a 1D mesh that conforms to the boundaries you describe above.
Then you create a submesh for each of the domains create a function-space, test trial functions etc for each domain/eq and then couple them through dS integrals (either with DG-type methods or Lagrange multipliers)…