convection_diffusion_stabilized
A 1D convection-diffusion problem

convection_diffusion_stabilized, a FENICS code which uses the finite element method to simulate the solution of a 1D convection-diffusion problem, using artificial viscosity to stabilize the solution.

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

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

Licensing:

The GNU LGPL license.

Reference:

1. Hans Petter Langtangen, Anders Logg,
   Solving PDEs in Python - The FEniCS Tutorial Volume 1.
2. Anders Logg, Kent-Andre Mardal,
   Lectures on the Finite Element Method.

Source Code:

• convection_diffusion_stabilized.py a script which sets up and solves the problem.
• convection_diffusion_stabilized.txt the output file.
• convection_diffusion_stabilized_mesh.xml the mesh to be used.
• convection_diffusion_stabilized_solution_grid10.png a plot of the solution for a grid of 10 elements.
• convection_diffusion_stabilized_solution_grid100.png a plot of the solution for a grid of 100 elements.