2026-10-09T19:13:40Zhttps://www.radar-service.eu/oai/OAIHandler10.35097/17912026-10-09T10:58:56Zradar4kit
https://dx.doi.org/10.35097/1791
Dörich, Benjamin
Henning, Patrick
Numerical experiments for "Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-κ regime" (v2)
Karlsruhe Institute of Technology
2023
Mathematics
dataset
Software
info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode
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 Figures2 and 3
#### Requirements
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
#### Figures
In the folder "code_23_DoerichHenning_GL" open a console and run the following commands after each other (2a+b, 4a+b can be executed in paralell).
1) Run "python3 c1_generate_rectangle.py"
2a) Run "python3 c2a_GL_FEM_comp_all_min_finest.py"
2b) Run "python3 c20_GL_FEM_comp_kappa20.py"
3) Run "python3 c2b_GL_FEM_comp_all_min.py"
4a) Run "python3 c3a_GL_FEM_comp_all_errors.py"
4b) Run "python3 c3b_GL_FEM_comp_all_eigs.py"
5) 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 2 and 3.
(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.
Ginzburg–Landau equation
superconductivity
error analysis
finite element method
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