heat_implicit
Time Dependent Heat Equation on Rectangle with Hole

heat_implicit, a FENICS script which uses the finite element method to solve a version of the time dependent heat equation over a rectangular region with a circular hole. The time steps are handled using an implicit solver.

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

1. cd $HOME/fenicsproject/heat_implicit
2. fenicsproject run
3. python3 heat_implicit.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:

• heat_implicit.py a script which sets up and solves the problem.
• heat_implicit_mesh.png a plot of the mesh.
• heat_implicit_solution_0.png
• heat_implicit_solution_2.png
• heat_implicit_solution_4.png
• heat_implicit_solution_6.png
• heat_implicit_solution_8.png
• heat_implicit_solution_10.png
• heat_implicit_solution_12.png
• heat_implicit_solution_14.png
• heat_implicit_solution_16.png
• heat_implicit_solution_18.png
• heat_implicit_solution_20.png