Biharmonic equation: Biharmonic equation — DOLFINx 0.10.0.0 documentation
Honestly, I can’t give you a full review of Galerkin based finite element methods.
I think a good source of information is: pde - What is the purpose of using integration by parts in deriving a weak form for FEM discretization? - Computational Science Stack Exchange.
Yes, if you want higher order regularity, you would need to use hermitian elements or splines.
You say that it is «as easy as». Sure, if someone has time to implement these elements, dofmaps and other constructs, similar to what was done in
an IGA library built on top of legacy fenics.
However, to make an efficient and maintainable implementation the developer has to been experienced with the fenics code structure, as well as the method they want to implement.
Since we are an open source project mainly driven by people in academic positions, we value any additional suggestions and proposals to improve the framework, and welcome external contributions.