[Gmsh] Refining a 4th order mesh to a 2nd order mesh

[Aman Saxena]

I have a 4th order mesh(with 5 points defining the lines) and I want to
refine it twice. As I refine it once, I get a linear mesh and all other
points except for the nodes forming the elements are lost.
So when I refine it for the second time it splits and gives me points on
the linear mesh which are not on the actual boundary. If I can get a 2nd
order mesh after refining the 4th order mesh, further refinement could have
given me points on the actual boundary.

Thus how to get a 2nd order mesh from the fourth order mesh?

I have attached a file to demonstrate this, figure 1 shows the boundary
element of fourth order mesh while second figure shows the boundary
element(linear) I get after one refinement and the last figure shows the
kind of element(quadratic -- degree 2) I want to have after one refinement.

I have also attached the mesh file.

Thanks.

 btc0-NLR-L3.v2.m4.msh.gz
<https://drive.google.com/file/d/1lUL_FqGF0EosFv5E95xUF764MVD6Ue3Y/view?usp=drive_web>
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