# Finite Element Solution of 1D Poisson Equation with Galerkin Spectral Decomposition

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This Demonstration shows the finite element method (FEM) applied to the solution of the 1D Poisson equation. A capacitor with plates at a fixed distance with each plate held at potential and , respectively, is shown on the right. The 1D Poisson equation for the potential is , with the charge density between the plates in the range for simplicity. The solution over the entire domain is subject to the Dirichlet boundary conditions (BCs): and .

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Contributed by: Jessica Alfonsi (University of Padova, Italy) (March 2011)

Open content licensed under CC BY-NC-SA

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The *Mathematica* program here has been adapted and extended from the Java code LaplaceFEM.java in the following book:

R. H. Landau, M. J. Paez, and C. C. Bordeianu, *A Survey of Computational Physics*, Princeton: Princeton University Press, 2008.

A standard reference for the basics of the finite-element method applied to electromagnetics is, for instance:

J. Jin, *The Finite Element Method in Electromagnetics*, 2nd. ed., New York: John Wiley and Sons, 2002.