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]> 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]>: > >> On Mon, 20 Apr 2015 18:25:03 +0200 >> Jan Blechta <[email protected]> wrote: >> >> > On Mon, 20 Apr 2015 16:00:52 +0000 >> > Anders Logg <[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]>: >> > > >> > > > 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]> 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]> >> > > >> *Sent:* 20 April 2015 13:46 >> > > >> *To:* Andrew McRae; Jan Blechta >> > > >> *Cc:* Joakim Bø; [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]>: >> > > >> >> > > >>> 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]> wrote: >> > > >>> >> > > >>>> On Fri, 17 Apr 2015 10:21:33 +0000 >> > > >>>> Joakim Bø <[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] >> > > >>>> http://fenicsproject.org/mailman/listinfo/fenics >> > > >>>> >> > > >>> >> > > >>> >> > > >> _______________________________________________ >> > > >> fenics mailing list >> > > >> [email protected] >> > > >> http://fenicsproject.org/mailman/listinfo/fenics >> > > >> >> > > >> >> > >> > _______________________________________________ >> > fenics mailing list >> > [email protected] >> > http://fenicsproject.org/mailman/listinfo/fenics >> >> _______________________________________________ >> fenics mailing list >> [email protected] >> http://fenicsproject.org/mailman/listinfo/fenics >> >
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