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VTK has had support for visualizing arbitrary-order Lagrange elements for a while now, but there aren't many resources out there (as far as I know) facilitating their use. Notably, these elements rely on a particular "onion-like" node ordering which many solvers (including mine) don't use by default. This means that people developing high-order solvers have to generate specific sets of visualization nodes which conform to such an ordering in order to use these VTK element types.

What I would really like is some way of generating unisolvent sets of nodes on reference (e.g. right-angled) triangles, tetrahedra, quadrilaterals, and hexahedra for a given polynomial degree, with the ordering given according to VTK's convention. Does such a tool exist? Even a database of hard-coded coordinates for different polynomial degrees (say, up to 10) would save me, and probably many others, a lot of time.

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  • $\begingroup$ Out of curiosity, why does the specific ordering bother you? It's just a permutation of any other ordering you might choose, and easy to put into a permutation table. $\endgroup$ Oct 31, 2022 at 3:54
  • $\begingroup$ @WolfgangBangerth I agree, reordering isn't conceptually difficult at all, but it requires generating and tabulating a permutation for every polynomial degree and element type, and I was trying to avoid having to do that if there was a faster way. As the nodes that I use for plotting can be arbitrary, I was interested in choosing them to be compatible with VTK's format without the need for reordering. $\endgroup$ Nov 1, 2022 at 11:48

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Such a tool exists, and I came across it a few weeks ago. In fact, it is mentioned in a comment of the linked post. Here is the repository: https://github.com/ju-kreber/paraview-scripts

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  • $\begingroup$ Thank you so much! This seems to be exactly what I was looking for. $\endgroup$ Nov 1, 2022 at 18:52

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