[Dune] GenericReferenceElements

[Carsten Graeser]

As I understood the old ReferenceElements are consistent w.r.t. to
subentities. I.e. if you use operator[j] of a subentity (i,c) it
should give you the same coordinates as operator[k] applied to the
element where k is the result of ref.subEntity(i,c,j,dim).

Due to the orientation change in the GenericReferenceElements
this is currently not true for the methods using the new numbering.

Consider for example the triangle numbering below.
 old            new
  2              2
  |\             |\
v1|  \0^       ^1|  \2^
  |    \         |    \
  0------1       0------1
     2>             0>

The switch of edge 0 and 2 is no problem since it is handeled e.g.
by indextranslation. But also the orientation of edge 1 is switched.
To ensure consistency you also have to switch the nodes (only) for
edge 1 which can not be done by indextranslation.

So if consistency should be preserved the GenericReferenceElements
must either preserve the oreintation or introduction of the new numbers
in a grid is much more delicate than expected.

Regard
Carsten

Carsten Graeser schrieb:
> Dear Dune,
> the new GenericReferenceElements do not only introduce a new numbering
> but also a use a different embedding of lower dim ReferenceElements.
> E.g. the edges in a triangle are oriented differently. This can be seen
> by checking the subEntity method in the (Generic-)ReferenrenceElements.
> 
> Is this the desired behaviour ? If yes this should be mentioned on
> the transition page. A complete solution would be the introduction
> of arrows in the subentity graphics to show the old and new orientation.
> 
> Carsten


-- 
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Carsten Gräser           | phone: +49-30 / 838-75349
Freie Universität Berlin | fax  : +49-30 / 838-54977
Institut für Mathematik  | email: graeser at math.fu-berlin.de
Arnimallee 6             |
14195 Berlin, Germany    | URL  : http://page.mi.fu-berlin.de/graeser
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