Implementing example for solving biharmonic equation in C++

Dear Developers and Maintainers,
I would like to implement an implementation of the biharmonic equation as a new problem in MFem, and attempt to implement it in base C.

The biharmonic problem is the equation
$\Delta^2u =f(x,y)$.

For my implementation, I will be using clamped boundary conditions.

$u(x,y)=0\in \partial \Omega$, $\nabla u(x,y)\cdot \hat{n}=0\in \partial \Omega$.
The weak form for this PDE is

$\int_{\Omega} \Delta u \Delta v=\int_{\Omega} fv$ .

Please let me know if you have any suggestions regarding this implementation or any specific considerations I should keep in mind.
Looking forward to your feedback!