Space-Time weak formulation

variational formulation
,
1

Hello dear community,
i’m new to FEniCSx.

I was wondering if it was actually possible to write the weak spacetime formulation as defined in this thesis document: https://theses.hal.science/tel-03810677v1/document

(Section 3.6.3, page 105 of the PDF file and page 86 of the thesis, author Israa Choucair)

By ‘Writing’ I mean:

  • Define the metric tensor g_{\mu \nu}
  • Define the Lie derivative \mathcal{L}
  • Define the variational form

then solve

Thanks in advance for taking your time to help me

PS. Apparently I cannot upload images nor share links. that’s why i formatted the link, hoping it’s gonna work
The document is :
Israa Choucair. A Four-dimensional Approach to Finite Element Method for the Large Transformations of Materials. Solid mechanics [physics.class-ph]. Université de Technologie de Troyes, 2021.
English. ffNNT : 2021TROY0025ff. fftel-03810677f

2

In principle, certainly. Here is a tutorial: Tutorial on Space-time FEM with FEniCSx

A problem I envision is the construction and use of the 4D meshes though.

3

This paper might be relevant: Redirecting
which had code published at:
FEniCS_Tensor_Product_Demos/demos/Problem1_Poisson_4D.ipynb at main · Markloveland/FEniCS_Tensor_Product_Demos · GitHub

1 Like
5

Thank you, I’ll take a look at that.

6

Thank you, I will read it.