[Gmsh] How to associate line elements on boundaries with inner elements

[Geordie McBain]

2011/12/1 jeremy theler <jeremy at talador.com.ar>:
>> I was a little puzzled by the first question in this thread, since in
>> the finite element method one does not need to know which domain
>> element a boundary element happens to be associated with in order to
>> carry out boundary integrals, or form their coefficients for imposing
>> boundary conditions during assembly.  Why do you need to know that
>> association?
>
> Not when dealing with essential (Dirichlet) boundary conditions.

No, not essential boundary conditions, I meant natural boundary
conditions, for which one has to `carry out boundary integrals'.
Actually often these days in finite element methods one approximates
Dirichlet conditions by Robin conditions with very high `conductance'
or `friction' so that all boundary conditions are natural and can be
treated in the same framework - but that's not the issue here.

> But for
> natural boundary conditions, you have to integrate the form functions over the
> surface where the natural conditions are given. For example, in a 2D problem,
> on the one hand you need the physical entity "line" to know what kind of
> boundary condition you have, and on the other you need to compute the form
> functions of the 2D element that contains the boundary.

Yes, but aren't the restrictions of the shape functions of your domain
elements to the boundary elements just the same as the
(n-1)-dimensional shape functions of the boundary elements?  This is
the case for classical linear triangular elements (Gmsh's elm-type 2),
for example.  That is, in many finite element applications, one can
simply use the boundary elements (as provided in the Gmsh .msh mesh
file, for example) without needing to know which domain elements
they're attached to...

> Can you see the point now?

No.

> I can give you some examples via private mail if you want.

Yes please.