dolfin team mailing list archive

[David Ham <David.Ham@xxxxxxxxxxxxxx>]

FWIW I agree with Martin that the element class needs to be able to
report this. For instance, if someone were to add non-equispaced
Lagrange polynomials which are typically used for higher order
computations, these need to show up as continuous, which would not
safely happen if you just check the element family.

A suggestion, if I may, which seems sort of mathematically nice to me
would be to define a SobolevSpace class. Instances of that class would
be comparable with each other and with element objects so one could
inquire whether an element has continuity in a given sense.

For instance there might be SobolevSpace objects H1, H1_div, H1_curl,
L_2. These would compare H1>H1_div>L_2,  H1>H1_curl>L_2.

A DG element object d would compare d<L_2 but false for any other inclusion.
A CG element would compare true for all the spaces.
RT1 would compare true for H1_div and L2 but not for H1_curl or H1 and so on.

Thought would need to be given to whether it is necessary to enforce
dimension matching properly or not.

In the Python level it might be more natural to make the inclusion
operator "in" rather than <.

Regards,

David



On 11 September 2012 18:20, Martin Sandve Alnæs <martinal@xxxxxxxxx> wrote:
> This is maybe cumbersome, but you can identify DG elements by checking
> the number of dofs per mesh entity through ufc::dof_map, with the function
>     /// Return the number of dofs associated with each cell entity of
> dimension d
>     virtual unsigned int num_entity_dofs(unsigned int d) const = 0;
> if
>   dm->num_entity_dofs(0) == dm->max_local_dimension()
> then no dofs are shared between elements.
>
> However this does not cover elements where dofs are shared but
> the functions are still discontinuous in certain senses.
> I guess more information will be needed in the ufc element classes.
>
> Martin
>
>
> On 11 September 2012 16:13, Garth N. Wells <gnw20@xxxxxxxxx> wrote:
>> On Tue, Sep 11, 2012 at 11:36 AM, Joachim Berdal Haga <jobh@xxxxxxxxx> wrote:
>>> Ok! I'll just check the element family then. Is there a more robust
>>> way to query it (in C++) than parsing
>>> f->function_space()->element()->signature()?
>>>
>>
>> The signature should not be used. It's not robust. Using the signature
>> has caused problems in the past.
>>
>> Garth
>>
>>> -j.
>>>
>>> On 11 September 2012 12:09, Kent-Andre Mardal <kent-and@xxxxxxxxx> wrote:
>>>> I guess it is only the Lagrange/CG element that is continuous. The others
>>>> are only continuous
>>>> in certain senses or directions. I don't think there is any meta data that
>>>> contains this
>>>> info.
>>>>
>>>> Kent
>>>>
>>>> On 11 September 2012 11:56, Joachim Berdal Haga <jobh@xxxxxxxxx> wrote:
>>>>>
>>>>> Is there a simple way to find out whether an arbitrary Function (or
>>>>> FunctionSpace) is continuous across cells in C++?
>>>>>
>>>>> -j.
>>>>>
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-- 
Dr David Ham
Department of Computing
Imperial College London

http://www.imperial.ac.uk/people/david.ham