dpg_laplace_adapt
Adaptive DPG Code for Poisson Problem

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.

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

  1. cd $HOME/fenicsproject/dpg_laplace_adapt
  2. fenicsproject run
  3. python3 dpg_laplace_adapt.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_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.

Reference:

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

Source Code:

Plots of the mesh are available at 7 levels of refinement:

Contour plots of the solution are available at 7 levels of refinement:

Last revised on 18 October 2018.