step11
Error Decay for a Sequence of Adaptive Meshes

step11, a FENICS script which uses the Discontinuous Petrov Galerkin (DPG) method to solve a Poisson problem, and repeatedly refines the mesh, guided by DPG error indicators. Two methods of adaptive refinement are compared, one of which refines cells which represent a fixed percentage of the error (case 0), and one of which refines a fixed percentage of the cells (case1). The problem uses a discontinuous diffusivity function kappa(x,y).

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

1. cd $HOME/fenicsproject/step11
2. fenicsproject run
3. python3 step11.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. Jay Gopalakrishnan,
   Five lectures on DPG Methods,
   Spring 2013, Portland State University,
   arXiv:1306.0557v2 [math.NA] 28 Aug 2014.

Source Code:

• step11.py the script.
• step11.txt the output file.

The error decay plots:

• step11_error_decay_case0.png
• step11_error_decay_case1.png

The mesh plots for case 0:

• step11_case0_mesh_level0.png
• step11_case0_mesh_level1.png
• step11_case0_mesh_level2.png
• step11_case0_mesh_level3.png
• step11_case0_mesh_level4.png

The mesh plots for case 1:

• step11_case1_mesh_level0.png
• step11_case1_mesh_level1.png
• step11_case1_mesh_level2.png
• step11_case1_mesh_level3.png
• step11_case1_mesh_level4.png