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Is there any software available which can directly render higher order finite element results? In particular, 3D finite elements would be preferable. It seems gmsh has some capability in this regard but am looking to explore more options.

Also, when I say "higher order" I mean rendering of quadratic and above elements. Tools like Paraview and VisIt seem to only render linear elements, and require mesh refinement and subsequent interpolation to a linear space to see the higher order solution, from what I understand.

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New versions of VTK support what you are asking for, and new versions of Paraview can also display this. The current version of Visit can not yet, though, at the time of writing this.

The trick is figuring out the specifics of how this should be described in the VTK file format. You can take a look at these two links to see the discussion and implementation of this feature in deal.II, along with some example images: https://github.com/dealii/dealii/issues/6931 https://github.com/dealii/dealii/pull/6994

(Disclaimer: I'm one of the principal developers of deal.II.)

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MFEM http://mfem.org and the associated visualisation tool supports several types of high order elements.

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