On Fri, Jan 29, 2010 at 10:31:05AM +0000, Garth N. Wells wrote: > > > 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.
Yes, it should work for any order. I was just questioning the usefulness of it if it results in standard P1 and P2 elements for k = 1,2. Then I think I understand how it all works. But does the FFC demo make any sense? Could we simplify it so that it just defines a finite element restricted to a facet and then some dS integral? It currently breaks the code we added for RestrictedElement yesterday because it has a complex nesting of restriction, then mixed with another element and then restricted again. It looks like this is not how you are using it in your solver. -- Anders
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