How to get the coordinates of dof with FE_Raviart_Thomas?

[Phạm Ngọc Kiên]

Hi colleagues,

With FE_Raviart_Thomas in 3D, the dofs are defined normal to the faces of each cell.

For example, if we use  FE_RaviartThomas(0), then in a cell we have 6 dofs defined on the 6 faces, and there is no dofs on the lines.

Do we have any way to get the dof coordinates and the direction of the shape function of the dof?

I would like to thank you very much in advance.

Best regards,

Kien

[Wolfgang Bangerth]

Pham,

> With FE_Raviart_Thomas in 3D, the dofs are defined normal to the faces of each
> cell.
> For example, if we use FE_RaviartThomas

> <https://www.dealii.org/current/doxygen/deal.II/classFE__RaviartThomas.html#adc8e64d0cdb38af6e29dc9ac0279f121>(0),

> then in a cell we have 6 dofs defined on the 6 faces, and there is no dofs on
> the lines.
> Do we have any way to get the dof coordinates and the direction of the shape
> function of the dof?

You can get the coordinates using DoFTools::map_dofs_to_support_points(). As
for the direction: That's something that the RT element does internally using
a convention that takes into account the two adjacent cells. I don't think
there is a way to determine this direction outside the element short of
evaluating the shape function at a point on the face.

Best
W.


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

[Phạm Ngọc Kiên]

Dear Prof. Wolfgang Bangerth,

The function fe.has_support_points() returns false. This means that the FE_Raviart_Thomas does not have support points.

I think generalized_support_points are used for this type of finite element.

For FE_RaviartThomas(0), are the dofs defined at the centers of the faces of a cell?

Is the order of the dofs the same as that of the faces. In that case, I think I can loop over the faces to evaluate the shape function at a point on each surface for the purpose of finding the direction.

Thank you very much for your guidance.

Best regards,

Kien

Vào Th 3, 24 thg 9, 2019 vào lúc 12:02 Wolfgang Bangerth <bang...@colostate.edu> đã viết:

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[Praveen C]

If you are going to use Cartesian meshes only, then you may want to check out

https://dealii.org/developer/doxygen/deal.II/classFE__RaviartThomasNodal.html

Best

praveen

[Wolfgang Bangerth]

On 9/23/19 11:12 PM, Phạm Ngọc Kiên wrote:
> The function fe.has_support_points() returns false. This means that the
> FE_Raviart_Thomas does not have support points.
> I think generalized_support_points are used for this type of finite element.

You are right -- the FE_RT is defined in terms of integrals on the faces, not
point values.


> For FE_RaviartThomas
> <https://www.dealii.org/current/doxygen/deal.II/classFE__RaviartThomas.html#adc8e64d0cdb38af6e29dc9ac0279f121>(0),

> are the dofs defined at the centers of the faces of a cell?

No, in fact they're not defined through interpolation at points at all, but
the degree of freedom is the integral along an entire face. But at least for
RT(0), that's only a constant multiple of the point value at the center of the
cell.

> Is the order of the dofs the same as that of the faces. In that case, I think
> I can loop over the faces to evaluate the shape function at a point on each
> surface for the purpose of finding the direction.

Yes, same order as the order of the faces of the cell.