Feature curved tetrahedron

[jfussbro]

Describe your changes here:

Enables usability of curved tetrahedral elements. Also fixes a bug in the readmshfile.

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[sandro-elsweijer]

Here are some first comments :)

[jmark]

LGTM! @sandro-elsweijer If you agree we can merge.

[sandro-elsweijer]

I think it would be best to wait for this, till the evaluations are completed. The usage of the advection solver is good for testing the code and some bugs could become observable :)

[jmark]

@jfussbro @sandro-elsweijer

I encountered a strange phenomenon when I computed interpolation nodes with curved triangles. I present you a (minimal) working example via a curved mesh around a cylinder. The respective files to reproduce the results are attached to this comment.

But first let me show what the problem is:

This is a scatter plots of interpolation nodes computed via the Julia interface T8code.jl which in turn is linked against the t8code library with the curved tri/tets merged in. I shifted one curved triangle into empty space on purpose to better show the details. The colors of each point represent the Jacobians at this point in space computed with the polynomial spanned by the interpolation nodes. Clearly the curved elements have some troubles. Even intersecting into neighboring elements. The refinement level is set to 0 in this case.

I did the same with a C++ version (attached to this comment) and got the same strange behavior:

To reproduce this please consider these files:
t8_features_curved_triangles_generate_cmesh_cylinder_2d.geo.txt
scatter_plot.cxx.txt
scatter_plot.gpi.txt

Note above C++ file is linked against t8code with curved tri/tets feature which in turn was merged with the current main. There was a change in the reference basis vectors for tris/tets which is not merged in this PR yet. The same erraneous behavior is observed with the old reference basis, too.