Locally divergence free FE space

[Praveen C]

Hello

Does deal.II have locally divergence-free finite elements ? I want each basis function to have zero divergence in each element and I do not require continuity of normal component.

Thanks

praveen

[Wolfgang Bangerth]

> Does deal.II have locally divergence-free finite elements ? I want each basis
> function to have zero divergence in each element and I do not require
> continuity of normal component.

I don't think we have any of these elements. What element in particular are
you thinking of?

Best
W.

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Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[Praveen C]

Hello Wolfgang

One example of locally divergence free basis is given on page 560 here

http://www.math.purdue.edu/~santos/research/disc_galerkin_ref/cockburn.pdf

I am trying to implement such space in deal.II.

Thanks

praveen

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[Wolfgang Bangerth]

> One example of locally divergence free basis is given on page 560 here
>
> http://www.math.purdue.edu/~santos/research/disc_galerkin_ref/cockburn.pdf

Interesting!

> I am trying to implement such space in deal.II.

That would certainly be of interest if you wanted to implement them. Let us
know if you have questions on how to implement a new element.

[Daniel Arndt]

Praveen,

I am not quite clear if those elements are of general interest for you or if you simply want to solve specific equations using these.

In the case of a Stokes problem or something similar a discontinuous pressure ansatz space should fulfill your needs. You might in particular have a look at http://www.dealii.org/developer/doxygen/deal.II/classFE__Q__DG0.html#a6eb900705fd9dab7c55be04968ccb41b

Best
Daniel

[Daniel Arndt]

I am just realizing that we are talking about different things when saying "locally divergence-free". So please forget about my comment.

[Praveen C]

Dear all

I would like some help on how to implement discontinuous locally divergence-free basis. I have written down the basis for degree=1 and 2 in the attached file.

What all do I need to implement for this type of space ?

Can you tell me if there is any existing FE space in deal.II which is close to this so that I can start modifying it ?

The basis functions are only for rectangular cells. 

Thanks

praveen