[Gmsh] Curved/second order element?

[Shi Jin]

Hi,

I read from the FAQ about the curved/2nd-order element:
" 5.8 Does Gmsh support curved elements?

Yes, Gmsh can generate both 1st order and 2nd order elements. To
generate second order elements, click on 'Second order' in the mesh
menu after the mesh is completed. To always generate 2nd order
elements, select 'Generate second order elements' in the mesh option
panel. From the command line, you can also use '-order 2'. "

 
However, as I tested, the generated 2nd order elements are actually the same straight-edged elements with the middle points added. What I have in mind is the curved element where the edge points are placed on the exact curved edge which is  different from the straight line connecting the two end points.

To make it clear, I am posting my geo and msh file.
In the geo file, I am testing a simple 2D circular arc:
element_dim = 1; 
Point(1) = {radius, 0, 0, element_dim} ;
Point(2) = {0, radius, 0, element_dim} ;
Point(3) = {0, 0, 0, element_dim};
Circle(1) = {1,3,2};
Line(2)={2,3};
Line(3)={3,1};
Line Loop(1) = {1,2,3};
Plane Surface(1) = {1};
Transfinite Line {1} = 2 Using Progression 1;

In the resulting msh file ( I chose the 'Second order' in the mesh
menu as suggested in the FAQ) is
$MeshFormat
2 0 8
$EndMeshFormat
$Nodes
6
1 1 0 0
2 0 1 0
3 0 0 0
4 0.5 0.5 0  !Note here: what I would like is 4 0.70711 0.70711 0
5 0 0.5 0
6 0.5 0 0
$EndNodes
$Elements
7
1 15 2 0 1 1
2 15 2 0 2 2
3 15 2 0 3 3
4 8 3 0 1 0 1 2 4
5 8 3 0 2 0 2 3 5
6 8 3 0 3 0 3 1 6
7 9 3 0 1 0 1 2 3 4 5 6
$EndElements

So I am wondering what is wrong with my procedure in order to get the curved element. Thank you very much.

Shi
--
Shi Jin, PhD