poisson_nonlinear
FENICS Solution of Nonlinear Poisson Equation

poisson_nonlinear, a FENICS script which uses the finite element method to solve a version of the nonlinear Poisson equation over the unit square.

The equation has the form

  - div( ( 1 + u^2 ) grad(u) ) = x * sin(y)  in Omega

  U = 1   if x = 1 on dOmega
  U = 0   otherwise on dOmega

Note that I have installed FENICS using Docker, and so to run this script I issue the commands:

1. cd $HOME/fenicsproject/poisson_nonlinear
2. fenicsproject run
3. python3 poisson_nonlinear.py
4. exit

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Reference:

1. Hans Petter Langtangen, Anders Logg,
   Solving PDEs in Python - The FEniCS Tutorial Volume 1.

Source Code:

• poisson_nonlinear.py a script which sets up and solves the problem.
• poisson_nonlinear.txt the output file.
• poisson_nonlinear_solution.png a plot of the solution.
• poisson_nonlinear_gradient.png a plot of the solution gradient.