I've started working on this issue:
https://bitbucket.org/fenics-project/ffc/issue/61/global-dofs-aka-reals-should-not-be

Can we agree on a target convention for naming of dofs in FEniCS?
I'd like to clean it up, and in the process get to know
the current dofmap implementation in dolfin better.

Here's my suggestion for terminology:

global dof numbering = numbering of dofs globally agreed upon across all
processes
local dof numbering = numbering of dofs local to a single process (*)
element dof numbering = numbering of dofs local to a single finite element
entity dof numbering = numbering of dofs local to a single mesh entity

global dofs = all dofs
local dofs = all dofs on a single process
element dofs = all dofs associated with a particular element (including its
subentities)
entity dofs = all dofs associated with a particular mesh entity (not
including its subentities)
facet dofs = dofs associated with a particular facet including its
subentities
universal dofs = dofs not associated with any mesh entity (constants, the
"Real" space)


So for example a dof associated with a vertex (0,i) is part of:
- the 'facet dofs' of facets (d-1,j) adjacent to vertex (0,i),
- the 'entity dofs' of vertex (0,i),
- the 'element dofs' of cells (d,k) adjacent to vertex (0,i),
- the 'local dofs' of the process that owns this dof,
- and the 'global dofs', unconditionally.

The new part here is the concept of a 'universal dof' which is part of:
- the 'element dofs' of all cells (**this is disputable),
- the 'local dofs' of the process that owns this dof,
- and the 'global dofs', unconditionally.
However the universal dof is NOT part of any entity dofs or facet dofs.

* It's not clear to me whether local dofs include ghosted dofs or not.

** The universal dof needs to be part of the element dofs at least for the
time being, unless we change a lot of code and handle them separately.
For constants that would be fine (and better in a lot of ways), but for
mixed
elements with a Real subspace that's trickyer.

Martin
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