[Dune] (no subject)

[Tatiana Voitovich]

Dear Andreas,

concerning the generic numeration for the reference elements,
to our believe, the simplexes are somewhat exceptional and
perhaps it is possible to treat them separately. For simplexes
we have found that is convenient to numerate the entities of codimention 1
with the use of the principle "opposite-to-which-node", e.g.
the side opposite to the node with the local number 1 has the number 1, ...
the side opposite to the node with the local number d+1 has the number d+1;
d=2,3.  Then for the codimention 1, the nodes that form the side opposite
to i
are the nodes that are not the same with i:
      {1,2,3,4}\{i}  in 3D,
      {1,2,3}\{i}     in 2D.
We thought however, that the convenient numeration for the edges is to
numerate them with the use of the numbers of the two nodes that form it.
But perhaps one could continue recursively with the "opposite-to-", knowing
the number of the "opposite" node (of the  whole simplex).

It is also very important (but I am sure it is implemented in the DUNE
like that)
that the nodes within the lists of the nodes corresponding to the simplex
itself,
to the list of the nodes corresponding to the codimention 1, etc., are
ordered
so that they form the "left turn", so that the determinant of the Vandermonde
matrix is grater then zero (this is specially important for the
implementation
of the finite volume and discontinuous Galerkin methods).

With my best regards, thanking you for creating the DUNE project,

Tatiana