Numerical experiments to "Error analysis of second-order local time integration methods for discontinuous Galerkin discretizations of linear wave equations"

The scripts are intended to reproduce the figures from the preprint

"Error analysis of second-order local time integration methods
for discontinuous Galerkin discretizations of linear wave equations"

by Constantin Carle and Marlis Hochbruck

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Requirements

The codes are tested with

Ubuntu 20.04.2 LTS and Python 3.8.10 and the following version of its modules:

numpy - 1.17.4
scipy

dolfin (fenics) - 2019.2.0.dev0 (including mshr)

matplotlib - 3.1.2
tikzplotlib - 0.9.6
pandas - 0.25.3

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Generation of figures

For the generation of Figure Y, Y=1,2,3, either execute the Python script 'script_figY.py'
in a suitable integrated development environment or run the command
python3 script_figY.py
in a terminal session.

For the generation of Figure 4 first execute the Python script 'script_fig4_data.py'
(via a suitable integrated development environment or in a terminal session)
which generates and saves the data for the figure.
To obtain the figure execute the script 'script_fig4_plot.py'
(the script 'script_fig4_plot_single.py' generates a different view of the data).

Additionally to the plots you can get the tikz-files which were used for
generating the figures in the preprint by setting the Boolean variable 'write_tikz'
from 'False' to 'True' at the beginning of the scripts.

The scripts for Figure 1, 2, 4 run in parallel on all available processors.
The number of used processors can be specified with the
variable 'num_processors_max' (integer). - 1.3.3