Numerical experiments for "error bounds for discrete minimizers of the ginzburg--landau energy in the high-$\kappa$ regime"

TechnicalRemarks: This program is intended to reproduce the results from the preprint

"Error bounds for discrete minimizers of the Ginzburg--Landau energy in the high-$\kappa$ regime" by Benjamin Dörich and Patrick Henning

The codes generates the lines in Figure 1

The program is tested with

Ubuntu 20.04.5 LTS and Python 3.8.10 and the following version of its modules:

• numpy - 1.17.4
• scipy - 1.3.3
• matplotlib - 3.1.2
• tikzplotlib - 0.9.8
• dolfin - 2019.2.0.dev0
• fenics - 2019.2.0.dev0

In the folder "CRC1173_Preprint_2023-11_Codes" open a console and run the following commands after each other (2a-c can be executed in paralell).

1) Run "python3 c1_generate_rectangle.py" 2a) Run "python3 c2_GL_FEM_comp_all_min.py" 2b) Run "python3 c16_GL_FEM_comp_kappa16.py" 2c) Run "python3 c20_GL_FEM_comp_kappa20.py" 3) Run "python3 c3_GL_FEM_comp_all_errors.py" 4) Run "python3 c4_GL_FEM_draw_error_plot.py"

After running the calculations, the files are stored as follows:

(a) the folder "plots_for_paper" contains the pdf and tikz files for the error plots in Figure 1. (b) the folders "sol_ref_3_Mag_st_2.0_kappa_[KAPPA]_P1_square" contain all figures of the solutions where [KAPPA] is replaced by the respective value.