MHB Examples of uses for the Poisson Eqn in 1d

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The discussion focuses on finding real-world examples of the 1D Poisson equation for a dissertation utilizing the finite element method. The original poster seeks practical applications rather than fabricated equations. A suggested application includes using Poisson's equation to determine potential fields from source charges in electricity and magnetism, as well as gravitational potential energy fields from masses. These examples highlight the equation's significance in physics. The conversation emphasizes the need for applicable scenarios to enhance the dissertation's relevance.
Carla1985
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Hi all,

I have almost finished my dissertation on using the finite element method to solve the 1D version of the Poisson equation. For the last section I would like to run through a couple of examples but am struggling to find some. Obviously I can make up any equations that satisfy the equation, this is what most of the exercises in the books are, but ideally I would like to use some that have real world value. Could anyone either suggest some examples or point me in the direction of some please.

Thanks
Carla
 
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Well, I don't know if you can shoe-horn such a problem into one dimension, but you use Poisson's equation to find the potential due to source charges in electricity and magnetism, and you can also use the exact same math to find the gravitational potential energy field due to an arrangement of masses. So it's of great importance!
 

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