FEniCS Tutorial: Poisson Equation

The Poisson Equation is arguably one of the simplest Partial Differential Equations (PDE) to solve. It forms the prototype for an elliptic PDE. There are many applications in physics like electric potentials or pressure correction equations in Computational Fluid Dynamics (CFD). Here, we will look at the simplest interpretation of a membrane under deformation. A unit square domain is fixed on all edges (=homogeneous Dirichlet Boundary Conditions) and a constant forcing is applied over the domain.

We are going to use the simplest options possible in FEniCS: A Lagrange Polynomial Function Space of first order.

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Timestamps:
00:00 Introduction
00:35 The Poisson Equation
01:01 Problem Setup
02:08 Weak Form
03:09 Imports
03:20 Constants
03:37 Some Boilerplate
03:55 Mesh & FEM discretization
05:20 Boundary Conditions
07:23 Trial & Test Functions
08:02 Weak Form
10:52 FEM Assembly and Linear Solve
12:30 Visualization
13:26 Discussion
14:37 Outro

[habib-ur-rehmaan]

Thank you very much for Poisson eq video, Can you pls make a video on SHEAR STRESS ( Deformation) on a Cube

[alikoulani]

assuming additional boundary condition at the center of the square = 0 (no force applying), how would this be implemented in the code?
also in case of two simulations running paralel, can the state of one be passed as the boundary condition to the other ?

[minhaanees]

Hi thank you so much.
Can you make video possion equation in discontinuous parameter/coffecient in one dimension