step8
Adaptive Refinement using DPG Error Indicators

step8, a FENICS code which uses the Discontinuous Petrov Galerkin (DPG) method to solve a Poisson problem, and repeatedly refines the mesh, guided by DPG error indicators.

The program relies heavily on the ideas and implementation embodied in Jay Gopalakrishnan's dpg_laplace code.

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

  1. cd $HOME/fenicsproject/step8
  2. fenicsproject run
  3. python3 step8.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:

Case 1:

Case 2:

Case 3:

Case 4:

Last revised on 02 November 2018.