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

**URL:** https://fenicsproject.discourse.group/t/is-it-possible-to-solve-original-or-weak-formulations-of-the-boundary-value-problems-in-dolfinx/16282
**Category:** dolfinx
**Created:** [November 12, 2024, 2:18pm UTC](https://fenicsproject.discourse.group/t/is-it-possible-to-solve-original-or-weak-formulations-of-the-boundary-value-problems-in-dolfinx/16282 "2024-11-12T14:18:11Z")
**Posts on this page:** 1
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### Author: ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)
#### Post date: [November 12, 2024, 11:26pm UTC](https://fenicsproject.discourse.group/t/is-it-possible-to-solve-original-or-weak-formulations-of-the-boundary-value-problems-in-dolfinx/16282/4 "2024-11-12T23:26:12Z")

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Biharmonic equation: [Biharmonic equation — DOLFINx 0.10.0.0 documentation](https://docs.fenicsproject.org/dolfinx/main/python/demos/demo_biharmonic.html)

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](https://scicomp.stackexchange.com/questions/7845/what-is-the-purpose-of-using-integration-by-parts-in-deriving-a-weak-form-for-fe#:~:text=bearing%20the%20same%20spirit%20with,not%20require%20integration%20by%20parts).

> [@marbor](#):
>
> - I used Lagrange continuous elements just for example purposes, taking care only about differentiability.  
> Firstly, sometimes continuity of the solution is not necessary. Secondly - if we were interested in continuous solution we could always use Hermitian or spline elements, couldn’t we?

Yes, if you want higher order regularity, you would need to use hermitian elements or splines.

> [@marbor](#):
>
> Put me right if I go astray, wouldn’t it be as easy as defining new function spaces/new types of finite element and appropriate operators to generate whole bunch of other numerical methods based on variational formulations if UFL could properly interpret the notation

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

> **[GitHub - david-kamensky/tIGAr: A Python library for isogeometric analysis (IGA)...](https://github.com/david-kamensky/tIGAr)**
>
> A Python library for isogeometric analysis (IGA) using FEniCS.

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.

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