Discontinuous Galerkin elements and other novel cell-types/function-spaces

Thank you @dcthomp for bringing up this topic. I found this link through this presentation. I am working on the post-processing of high-order methods, specifically the spectral difference method and the discontinuous Galerkin Spectral Element Method, both used in the CFD community. A particularity of these methods is that the approximation is done cell-wise (as in DG methods) and that the degrees of freedom are not associated with the nodes of cell geometry.
I have a very similar wish-list to that of @jfausty, namely

  • hp adaptive meshes (h-adaptivity: how to handle the hanging nodes?, p-adaptivity:post-processing algorithms with curved cells?)
  • non-isoparametric elements
  • adaptive refinement to obtain a linear visualization mesh
  • modal approximations

I have quite some experience with the method used by Gmsh, but it has its limits. I am super interested in ongoing developments on the side of VTK/ParaView, and I am eager to discuss them with you.