step4
Use Symbolic Package for Right Hand Side of Poisson Equation

step4, a FENICS code which shows how to generate a formula for f(x,y), the right hand side of a Poisson problem, by applying the symbolic mathematics package to a formula for the desired exact solution u(x,y).

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

1. cd $HOME/fenicsproject/step4
2. fenicsproject run
3. python3 step4.py
4. exit

Licensing:

The GNU LGPL license.

Related Data and Programs:

dpg_bvp, a FENICS script which uses the Discontinuous Petrov Galerkin (DPG) method to solve a boundary value problem over an interval, by Jay Gopalakrishnan.

dpg_laplace, a FENICS script which uses the Discontinuous Petrov Galerkin (DPG) method to solve a Poisson problem over the unit square, by Jay Gopalakrishnan.

dpg_laplace_adapt, a FENICS script which uses the Discontinuous Petrov Galerkin (DPG) method to solve a Poisson problem over the unit square, with adaptivity, by Jay Gopalakrishnan.

Reference:

1. Jay Gopalakrishnan,
   Five lectures on DPG Methods,
   Spring 2013, Portland State University,
   arXiv:1306.0557v2 [math.NA] 28 Aug 2014.

Source Code:

• step4.py applies the DPG method to a Poisson problem.
• step4.txt the output file.
• step4_u_contour.png a contour plot of the solution.