[vtkusers] Higher order element visualization

[David Thompson]

Hi Andrew,

> I am working on a finite element visualization of simulations that uses arbitrary order monomial shape functions. Currently, we are visualizing the results with a single value on a cell, but we would like to write out the monomial coefficients and do a proper projection of the solution. Is this something that is possible with VTK? If it is, we are happy to write some custom code, but would like a nudge in the correct direction.

Monomial shape functions are not numerically stable. There is some work[1,2] to extend VTK to handle arbitrary order Lagrange shape functions (also not numerically stable). Ideally, Legendre or spline-basis interpolation would be used and other bases would be projected to it.

	David

[1]: https://gitlab.kitware.com/dcthomp/vtk/commits/lagrange-progess
[2]: https://gitlab.kitware.com/tjcorona/vtk/commits/lagrange-elements