Papers › Vortex-capturing multiscale spaces for the Ginzburg-Landau equation

Vortex-capturing multiscale spaces for the Ginzburg-Landau equation

23 May 2024arXiv:2405.14772links table onlyarchive 2025-07-28

Maria Blum, Christian Döding, Patrick Henning

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

This paper considers minimizers of the Ginzburg-Landau energy functional in special multiscale spaces that are based on finite elements. The spaces are constructed by localized orthogonal decomposition techniques and their usage for solving the Ginzburg-Landau equation was first suggested in [D\"orich, Henning, SINUM 2024]. In this work we further explore their approximation properties and give an analytical explanation for why vortex structures of energy minimizers can be captured more accurately in these spaces. We quantify the necessary mesh resolution in terms of the Ginzburg-Landau parameter κ and a stabilization parameter β≥0 that is used in the construction of the multiscale spaces. Furthermore, we analyze how κ affects the necessary locality of the multiscale basis functions and we prove that the choice β=0 yields typically the highest accuracy. Our findings are supported by numerical experiments.

PaperPDFCode

Code

cdoeding/GinzburgLandauLOD officialmentioned in paper report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections