MHB Examples of uses for the Poisson Eqn in 1d

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SUMMARY

The discussion focuses on the application of the Poisson equation in one dimension, particularly using the finite element method for solving real-world problems. Carla seeks examples that provide practical value rather than hypothetical scenarios. A key insight shared is that Poisson's equation can be utilized to determine the potential from source charges in electricity and magnetism, as well as to calculate gravitational potential energy fields from mass arrangements. These applications underscore the significance of the Poisson equation in both physics and engineering contexts.

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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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