On 9/18/25 02:56, Tom Jackson wrote:
I am a student working on a project involving fourth-order PDEs (specifically,
Kirchhoff plate problems), where C1-continuous finite elements are
traditionally used. I understand that deal.ii does not have built-in C1
elements, and my project would benefit greatly from the *Hsieh-Clough-Tocher
(HCT)* element.
Therefore, I am writing to explore the feasibility of implementing the HCT
element myself. My current understanding is that this would require creating a
new class, `FE_HCT`, and defining its behavior in corresponding `fe_hct.h` and
`fe_hct.cc` files, following the instructions in /The deal.II FAQ/ :
/“The actual implementation would most conveniently start from the `FE_Poly`
class. You first implement the necessary polynomial space in the base library,
then you derive `FE_Your_FE_Name` from `FE_Poly` (using your new polynomial
class as a template) and add the connectivity information.”/
I would greatly appreciate any high-level guidance on the implementation
process, the potential challenges of developing such a complex composite
element, and whether it is realistically feasible for an individual developer
to accomplish this task.
Thank you for your time and for maintaining this excellent library. Insights
you can provide on the implementation path or feasibility analysis would be
immensely helpful.
Tom:
it is certainly feasible to write a new element. Plenty of people have done
it. That said, the key problem with these C^1 elements is that their degrees
of freedom involve derivatives, and it is difficult to implement things in a
way that allows solving problems on more than a uniformly structured grid. I
would expect someone without prior experience in writing elements to spend
several months of full-time work on this (perhaps in the range of 3-6 months,
but maybe not more than that). We would be happy to help out with questions,
of course.
That said: There are several tutorial programs that show how to solve
fourth-order problems without using "exotic" elements. What is stopping you
from using those?
Best
W.
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