> I am using discontinuous elements on a regular mesh.  Given a degree of
> freedom that I know lies on a given cell and face (technically has
> support on that face, as this is dG) I would like to find out which dof
> is its neighbour i.e. the equivalent dof from the cell adjoining across
> the given face.
>
> It is not difficult to loop through all of the cells, then faces then
> dofs and find the dofs with support on a given face.  It is not
> difficult to then extract the neighbouring cell and find which dofs from
> that cell also lie on the face.  However, what is the best way to find
> which dof matches which dof.  For example, in 2d using linear dG
> elements each face has 2 dofs with support on that face from one cell,
> and two from the neighbouring cell.  I would like to know how they are
> matched so I can add constraints.

If you are using the FE_DGQ class, then shape functions are interpolation 
polynomials which are associated with interpolation points. We call them 
support_points in deal.II. You may want to read up on the functions
  FiniteElement::get_unit_support_points
  FiniteElement::get_face_unit_support_points
and see if that is useful to you -- comparing face support points for two 
shape functions should allow you to identify the matching ones, together with 
the things you've already found out so far.

Best
 W.

-------------------------------------------------------------------------
Wolfgang Bangerth                email:            [email protected]
                                 www: http://www.math.tamu.edu/~bangerth/

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