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## Re: [Getfem-users] quadratic mesh, step 2

 From: Edouard Oudet Subject: Re: [Getfem-users] quadratic mesh, step 2 Date: Fri, 4 Jan 2019 09:54:42 +0100 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Thunderbird/60.2.1

```Dear Yves,
Thanks, that sounds perfect for me!
```
Just to be sure: Gauss integration points are inside points of the curved convex where the fem are smooth?
```All the best,
Edouard.

Le 02/01/2019 à 13:57, Yves Renard a écrit :
```
```Dear Edouard,

If you need to evaluate the gradient on the center of a triangle, the best way
is to interpolate it on a P0 fem, because its degree of freedom are located on
the center of the triangle. Moreover, in that case, there is no inversion and
the interpolation is fast (you can have location of dofs with mf.dof_nodes()
method). You can either interpolate any value on the Gauss points of an
integration method with the mim_data object, which is also fast. But, for the
moment, there is no mean to interpolate on a point with its coordinates on the
reference element, unfortunately.

Best regards,

Yves

----- Original Message -----
Sent: Monday, December 31, 2018 6:44:30 PM
Subject: Re: [Getfem-users] quadratic mesh, step 2

Dear Yves,

Thanks a lot for your answer, that's perfectly clear now.. and works!

One more question: working on triangulated (curved) surface in R^3, I am
interested to evaluate the gradient of a fem function at some point of
this curved mesh. When my mesh was flat I used to build a model and call
the interpolation of "Grad_u" on my mesh at a point P which was inside
of the mesh.

Now that the mesh is curved, it is more tricky to produce a point which
is exactly on the curved mesh like, for instance, the center of a curved
triangle. Here are my (I hope last) questions:

1) Is it possible to generate points inside of a curved convex cell
described by a mesh?
2) How to interpolate the gradient at these points. Does the same
procedure work even if the point is never exactly on the curved mesh ?

Thanks a lot for your work and Happy new Year !!!

Best,

Edouard.

Le 29/12/2018 à 20:47, Yves Renard a écrit :
```
```Dear Edouard,

The point ordering is the same that the corresponding fem. You can see the dof
ordering of fem in the page

http://getfem.org/userdoc/appendixA.html

And yes, of course, it is possible to also mesh curved surfaces in 3D.

Best regards,

Yves

----- Original Message -----
Sent: Saturday, December 29, 2018 8:05:04 PM
Subject: [Getfem-users] quadratic mesh, step 2

I answer to the first part of my question: curved mesh seem to be
implemented regarding examples in the tests/meshes folder. Great!!
My remaining questions are:
1) How/where is defined the ordering point sequence which defines a
curved convex cell in a getfem-mesh file?
2) curved mesh seem to be implemented in 2D, 3D but is it also the case
for surfaces (triangulation in 3D)?
Thanks!
```
```
--
Edouard Oudet : http://www-ljk.imag.fr/membres/Edouard.Oudet/
IMAG - Bureau 164
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```