ffc team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

Anders Logg wrote:
> On Fri, Jan 29, 2010 at 10:10:37AM +0000, Garth N. Wells wrote:
> 
>>> Sub domains seem to be very different, but the other two cases just
>>> seem to be a matter of some dofs being "active" and the other zeroed
>>> out. This is what Marie suggested yesterday, that a restricted element
>>> only considers a subset of the dofs of some given element.
>>>
>> Sounds good.
>>
>>> The thing I don't understand yet is the selection of which dofs should
>>> be active. If we think of the case with restriction to facets, then
>>> the element needs to be restricted to different facets depending on
>>> which facet we are integrating over, or are we always mapping one
>>> specific facet of the reference cell to the current facet?
>>>
>> It works the same way as the DG elements, just the internal dofs are
>> thrown away, which is the latter if the above, right?
>>
>>> Say we have P1 elements in 2D which have 3 dofs. Then we could
>>> restrict that element to the dofs on the first facet (facet 0). These
>>> dofs are then labeled 1 and 2. But sometimes a facet in the mesh will
>>> correspond to the edge between 0 and 1 or 0 and 2.
>>>
>> We don't restrict to individual facets, but to all facts of a cell.
> 
> That makes sense, but one thing still confuses me. Say that we have a
> P1 element and restrict it to facets. Then all dofs are on the facets
> so the result of the restriction is just a new P1 element. Same for P2
> where the result again is a new P2 element. 

Yes.

> For P3, the result is P3
> element minus just one dof.

Yes.

> So does this make much difference for
> other than very high degree elements?
>

It is only needed for k > 2. It's important because everything in
FFC/UFL works for arbitrary orders.

Garth

> --
> Anders