Simulation of the Poisson Equation on a Unit Line | FEATool Multiphysics Tutorial

The classic Poisson equation is one of the most fundamental partial differential equations (PDEs). Although one of the simplest equations, it is a very good model for the process of diffusion, and comes up in many applications (for example fluid flows, heat transfer, and chemical transport problems). It is therefore fundamental to many simulation codes to be able to solve it efficiently and accurately.

This example shows how to set up and solve the Poisson equation for a scalar field u = u(x) on a unit line. Both the diffusion coefficient D and source term f are assumed to be constant and equal to 1. Homogeneous Dirichlet boundary conditions, u = 0, are prescribed on all boundaries of the domain. One can derive an exact analytical solution for this problem u(x) = (-x^2+x)/2, which is used to measure the accuracy of the computed solution.

► QUICK LINKS:
00:00 - Introduction
02:20 - Geometry definition
03:05 - Mesh generation
03:45 - Equation specification
04:45 - Boundary conditions
05:55 - Solving
06:40 - Postprocessing and visualization

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