Anisotropic fe space

[Praveen C]

Hello

I want a space of polynomials like Q_{r,s} where the degree is r in one direction and s in another direction. Discontinuous is fine. I know one can construct anisotropic quadrature rules, but I dont see a way to get an fe space. FE_DGQArbitraryNodes seems to need same degree in all directions.

Thanks

praveen

[Jean-Paul Pelteret]

Hi Praveen,

I'm a little bit naïve when it comes to these things, but can you not achieve this by using an FESystem with each component given by a different FE and ensuring that all components are fully coupled?

Regards,

Jean-Paul

[Praveen C]

Hello Jean-Paul

I am working with Raviart-Thomas spaces. For degree k, the x component of the vector field would have degree (k+1) in x variable and degree k in y variable, i.e., it is in Q_{k+1,k}. Similarly the y-component is in Q_{k,k+1}. This is already provided in FE_RaviartThomasNodal.

I need the test functions for the moments, and these test functions which live in Q_{k-1,k} for x-component and in Q_{k,k-1} for y-component.

Best

praveen

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[Wolfgang Bangerth]

On 08/28/2017 06:51 AM, Praveen C wrote:
>
> I am working with Raviart-Thomas spaces. For degree k, the x component of the
> vector field would have degree (k+1) in x variable and degree k in y variable,
> i.e., it is in Q_{k+1,k}. Similarly the y-component is in Q_{k,k+1}. This is
> already provided in FE_RaviartThomasNodal.
>
> I need the test functions for the moments, and these test functions which live
> in Q_{k-1,k} for x-component and in Q_{k,k-1} for y-component.

Since you already found how the FE_RaviartThomas does it, can you not use the
same approach for your element?

Best
W.

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

[Praveen C]

Yes, I could use FE_RaviartThomasNodal<dim>(k-1) to get the test functions, though I would have liked to choose other nodes.

Thanks

praveen

[Wolfgang Bangerth]

On 08/28/2017 09:42 AM, Praveen C wrote:
> Yes, I could use FE_RaviartThomasNodal<dim>(k-1) to get the test
> functions, though I would have liked to choose other nodes.

Then I don't think I understand what the original question was. Do you
need an element, or just the polynomials? For the latter, you can still
see how FE_RTNodal constructs the polynomials it then uses as its shape
functions.

[Praveen C]

Well, when I asked the question, I did not know how to do it. I then saw from my own answer to Jean-Paul's question that I could use a lower degree FE_RaviartThomasNodal itself to get test functions for moments.

Thanks

praveen