How to Implement First and Second Derivatives w.r.t. Specific Directions in FEniCS

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@Great_Mammuth

When using the terms inner and grad, the solution is similar to the one obtained from Mathematica. However, when I use the terms f.dx(0).dx(0)

One doesn’t use the strong form of a PDE in the finite element method. One of the key aspects of FEM is that you set up a weak formulation (variational form), where you lessen the requirement of the function spaces used for your unknown). This has for instance been discussed in

Is it possible to solve original or weak formulations of the boundary value problems in DOLFINx?

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 tim…

referring to pde - What is the purpose of using integration by parts in deriving a weak form for FEM discretization? - Computational Science Stack Exchange