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
.
Contributed by: Jessica Alfonsi (University of Padova, Italy) (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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.
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