dpg_bvp
Discontinuous Petrov Galerkin for a Boundary Value Problem

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

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

1. cd $HOME/fenicsproject/dpg_bvp
2. fenicsproject run
3. python3 dpg_bvp.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.

Related Data and Programs:

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:

• dpg_bvp.py applies the DPG method to a boundary value problem.
• dpg_bvp.txt the output file.
• dpg_bvp.pdf a plot comparing the DPG, Least Squares, and L2 solutions;
• dpg_bvp.mat a MATLAB datafile storing the PG, LS, L2, and Exact solution values.
• dpg_bvp_original.py the original version of the script.