Hi, Greg here from Coreform! We are friendly towards open-source solvers. We're unable to open-source Cubit (though we've looked into this quite extensively) because if we took out all the 3rd-party functionality that we can't open-source, Cubit would no longer be Cubit! But we certainly want to be friendly with open-source solvers -- we've contributed to ParaView (adding support for Bezier cells to visualize splines / IGA), libMesh (open-source FEM framework), MOOSE, and SEACAS/Exodus.
On that note, I would say that Cubit *natively* supports the open-source mesh format: Exodus. Exodus is part of the open-source
"Sandia Engineering Analysis Code Access System" (SEACAS) project. Given Cubit's long history at SNL, it's probably no surprise that Cubit was developed primarily to build Exodus mesh files for SNL's simulation codes. I'm admittedly not as familiar with Elmer as I am other codes, but it should be fairly straightforward to support Exodus in Elmer if it's not already.
In my former life, I found Exodus to be quite powerful for analysis - that SEACAS link talks about the gluttony of utilities for Exodus, from domain-decomposition & domain-recomposition, to ASCII conversion, Matlab converters, a Python module, variable remapping, and more. Plus Exodus stores not only the mesh for the simulation, but also the simulation results... and it's natively supported by ParaView (by default ParaView applies the "warp vector" within its Exodus reader, and it even has a simple option to draw mode shapes if provided). In fact, while the format is technically called "Exodus" users will often refer to the input-mesh file as a "Genesis" file (note the biblical reference) and the output-mesh with results as "Exodus".
On the note of p-elements, we're also adding our U-spline technology to Coreform Cubit - which we plan to also make available in Coreform Cubit Learn. And Coreform Cubit will be able to export the Bezier extraction operator, which allows for a traditional FEM solver to access spline finite elements. So you
could build a cubic U-spline, whose matrix
is easier to solve (even easier than a linear element's global matrix).