ufl team mailing list archive

[Marie Rognes <meg@xxxxxxxxx>]

On 01. okt. 2010 15:54, Anders Logg wrote:
> On Wed, Sep 29, 2010 at 08:31:51PM -0500, Douglas Arnold wrote:
>   
>> FEniCS/UFL uses historical element names, like Raviart-Thomas,
>> Nedelec 1st kind H(div), etc.  These have to be learned, although
>> this is fortunately ameliorated somewhat by having some
>> synonyms, like N1curl.  It can also cause confusion sometimes,
>> as the names are not always used consistently in the literature
>> (and I think that "Discontinuous Lagrange" is a contradiction
>> in terms).
>>
>> However there is a systematic, consistent way to refer to
>> the majority of elements available, so I am making the
>> suggesting that this systematic form be added as
>> an additional option.  The systematic way is what is
>> used in the Finite Element Exterior Calculus, namely the
>> two families, which are in denoted in LaTeX by
>> $P_r\Lambda^k$ and $P_r^-\Lambda^k$, defined for
>> polynomial degree r=1,2,... and form degree k between
>> 0 and n on simplices of dimension n.  Thus I am suggesting
>> adding something like
>>
>>   V = FunctionSpace(mesh, "P Lambda", r, k)
>> and
>>   V = FunctionSpace(mesh, "P- Lambda", r, k)
>>
>> The translation to current names is:
>>
>>   {"P Lambda", r, 0} and {"P- Lambda", r, 0} coincide and
>>      are equal to {"Lagrange", r}
>>   {"P Lambda", r, n} is the same as {"Discontinuous Lagrange", r}
>>   {"P- Lambda", r, n} is the same as {"Discontinuous Lagrange", r-1}
>>   {"P- Lambda", r, 1} is {"Nedelec 1st kind H(curl)", r}
>>   {"P Lambda", r, 1} is {"Nedelec 2nd kind H(curl)", r}
>>   {"P- Lambda", r, n-1} is {"Nedelec 1st kind H(div)", r}
>>   {"P Lambda", r, n-1} is {"Nedelec 2nd kind H(div)", r}
>>     
> Sounds good to me.
>
>   
>> I want to stress that there is nothing arbitrary about this.
>> The whole family of P Lambda and P- Lambda spaces can be
>> defined at once for all r, k, n.  This even works for n=1
>> and n>3 (although the latter are not yet implemented in
>> FEniCS).
>>     
> (They are, but only in the experimental Exterior package.)
>
>   
>> There is a small issue in 2D where n-1 = 1, so the last
>> two cases conflict with the preceding two.  This is the
>> choice between the rotated Raviart-Thomas or Brezzi-Douglas-Marini
>> elements or the usual ones in 2D.  I would suggest always
>> thinking of 1-forms as the images of gradients, and hence
>> 1-forms always correspond to H(curl), also in 2D.
>>
>> What do you all think?
>>
>>   -- Doug
>>
>> P.S. On Marie's suggestion, I am posting this both to
>> the UFL and the FEniCS mailing lists.
>>     
> I have added a blueprint for this:
>
> https://blueprints.launchpad.net/ufl/+spec/exterior-calculus-names/
>
> And assigned it to the appropriate person ;-)
>   


The assignee will fix after we actually support (P Lambda, q, 3, 1)

--
Marie