As Martin++ say, it should be straightforward to implement by dofs of lagrange and p0. While it is not a fem space, it is a function space as the basis is linearly independent. It might also be quite useful as it relates to dual mesh. The jump operators in ufl will however likely be messed up.
On Monday, 20 April 2015, Andrew McRae <[email protected]> wrote: > Of course, for large meshes the opposite happens. For a UnitSquareMesh(n, > n), the number of vertices (and hence dimension of the space) is (n+1)^2, > while the number of cells is 2n^2. > > On 20 April 2015 at 17:44, Anders Logg <[email protected] > <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: > >> The way I see it, the global space would have 4 basis functions on the >> mesh consisting of two triangles, but the dimension of the space is still >> 2, meaning in particular that the mass matrix would be singular. (Which >> does not necessarily imply that this type of "element" would not be useful >> for anything.") >> >> -- >> Anders >> >> >> mån 20 apr. 2015 kl 18:31 skrev Jan Blechta <[email protected] >> <javascript:_e(%7B%7D,'cvml','[email protected]');>>: >> >>> On Mon, 20 Apr 2015 18:25:03 +0200 >>> Jan Blechta <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: >>> >>> > On Mon, 20 Apr 2015 16:00:52 +0000 >>> > Anders Logg <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: >>> > >>> > > Yes, it might actually be that simple: The elements would be >>> > > standard P1 elements with the only difference that the value of the >>> > > basis functions are always one (each triangle has 3 basis function >>> > > and each is = 1) and all derivatives are zero. >>> > >>> > This element does not make a sense with this definition. Imagine 2D >>> > mesh of two triangles. There are 4 "basis" functions while the >>> > dimension of the space is 2. In the other words, these "basis" >>> > functions are not linearly independent hence they don't form a basis. >>> >>> In other words, span of suggested "basis" functions is exactly the >>> usual space of piece-wise constants. That's why it is not used as a FE >>> space. Rather as a transform for operator lumping. >>> >>> Jan >>> >>> > >>> > Jan >>> > >>> > > >>> > > Might be possible to "hack" by modifying >>> > > _create_fiat_element(ufl_element) in ffc/fiatinterface.py. >>> > > >>> > > -- >>> > > Anders >>> > > >>> > > >>> > > mån 20 apr. 2015 kl 17:44 skrev Martin Sandve Alnæs >>> > > <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>>: >>> > > >>> > > > Doesn't sound that hard. Basically dofmaps like CG1 elements with >>> > > > basis functions replaced by 1.0 on the entire support? >>> > > > On 20 April 2015 at 15:37, Joakim Bø <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: >>> > > > >>> > > >> Thanks for answering! >>> > > >> >>> > > >> >>> > > >> Anders got it right, discontinous and overlapping basis >>> > > >> functions with the same global support as P1 tent functions. >>> > > >> Sorry to hear that it would be hard to implement, but it came as >>> > > >> no surprise... >>> > > >> >>> > > >> >>> > > >> Thanks anyway! >>> > > >> >>> > > >> >>> > > >> Joakim >>> > > >> >>> > > >> >>> > > >> -- >>> > > >> Joakim Bø >>> > > >> Prosjektleder ENT3R UiO >>> > > >> Tlf.: 915 24 326 >>> > > >> >>> > > >> http://www.ENT3R.no/OSLO >>> > > >> ------------------------------ >>> > > >> *From:* Anders Logg <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> >>> > > >> *Sent:* 20 April 2015 13:46 >>> > > >> *To:* Andrew McRae; Jan Blechta >>> > > >> *Cc:* Joakim Bø; [email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');> >>> > > >> *Subject:* Re: [FEniCS] Implement a new finite element type for >>> > > >> testing purposes? >>> > > >> >>> > > >> If I understand correctly, you want discontinuous and >>> > > >> overlapping basis functions with the same global support as the >>> > > >> P1 tent functions. Unless you find a clever trick for how to >>> > > >> treat this (perhaps via some linear algebra using P0 elements in >>> > > >> combination with some suitable constraints), this looks >>> > > >> difficult to implement in FEniCS. We assume each element is >>> > > >> defined locally on triangles/tetrahedra. >>> > > >> >>> > > >> -- >>> > > >> Anders >>> > > >> >>> > > >> >>> > > >> mån 20 apr. 2015 kl 13:14 skrev Andrew McRae >>> > > >> <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>>: >>> > > >> >>> > > >>> I interpret it as a DG0, but where nodes are associated with >>> > > >>> vertices. Related to mass-lumping, I guess. >>> > > >>> >>> > > >>> On 20 April 2015 at 12:07, Jan Blechta >>> > > >>> <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: >>> > > >>> >>> > > >>>> On Fri, 17 Apr 2015 10:21:33 +0000 >>> > > >>>> Joakim Bø <[email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');>> wrote: >>> > > >>>> >>> > > >>>> > Hi! >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > I am in need of a new type of basis function for testing >>> > > >>>> > purposes. It is much similar to the basis functions of the >>> > > >>>> > Taylor-Hood P1 element, the difference is that the functions >>> > > >>>> > are piecewise constant equal to 1 in this "local >>> > > >>>> > domain" (similar for 1D and 3D): >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > [http://www.fsz.bme.hu/~szirmay/radiosit/rad10.gif] >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > and zero in the rest of the domain. In general, phi_i = 1 for >>> > > >>>> > "local domain of dof i", 0 else. >>> > > >>>> >>> > > >>>> If I understand your explanation correctly (it does not seem to >>> > > >>>> match with the figure!), it is Discontinuous Lagrange element >>> > > >>>> of degree 0, which is implemented. >>> > > >>>> >>> > > >>>> Jan >>> > > >>>> >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > Would it be possible to implement this without too much work? >>> > > >>>> > Or would it require a lot of effort? >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > Thanks! >>> > > >>>> > >>> > > >>>> > Joakim >>> > > >>>> > >>> > > >>>> > >>> > > >>>> > -- >>> > > >>>> > Joakim Bø >>> > > >>>> > Prosjektleder ENT3R UiO >>> > > >>>> > Tlf.: 915 24 326 >>> > > >>>> > >>> > > >>>> > http://www.ENT3R.no/OSLO >>> > > >>>> >>> > > >>>> _______________________________________________ >>> > > >>>> fenics mailing list >>> > > >>>> [email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');> >>> > > >>>> http://fenicsproject.org/mailman/listinfo/fenics >>> > > >>>> >>> > > >>> >>> > > >>> >>> > > >> _______________________________________________ >>> > > >> fenics mailing list >>> > > >> [email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');> >>> > > >> http://fenicsproject.org/mailman/listinfo/fenics >>> > > >> >>> > > >> >>> > >>> > _______________________________________________ >>> > fenics mailing list >>> > [email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');> >>> > http://fenicsproject.org/mailman/listinfo/fenics >>> >>> _______________________________________________ >>> fenics mailing list >>> [email protected] >>> <javascript:_e(%7B%7D,'cvml','[email protected]');> >>> http://fenicsproject.org/mailman/listinfo/fenics >>> >> >
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