KIT | KIT-Bibliothek | Impressum | Datenschutz

A multiscale approach to the stationary Ginzburg–Landau equations of superconductivity

Döding, Christian; Dörich, Benjamin ORCID iD icon 1; Henning, Patrick
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

In this work, we study the numerical approximation of minimizers of the Ginzburg– Landau free energy, a common model to describe the behavior of superconductors under magnetic fields. The unknowns are the order parameter, which characterizes the density of superconduct- ing charge carriers, and the magnetic vector potential, which allows to deduce the magnetic field that penetrates the superconductor. Physically important and numerically challenging are especially settings which involve lattices of quantized vortices which can be formed in materials with a large Ginzburg–Landau parameter $\kappa$. In particular, $\kappa$ introduces a severe mesh resolution condition for numerical approximations. In order to reduce these computational restrictions, we investigate a particular discretization which is based on mixed meshes where we apply a Lagrange finite element approach for the vector potential and a localized orthogonal decomposition (LOD) approach for the order parameter. We justify the proposed method by a rigorous a-priori error analysis (in $L^2$ and $H^1$) in which we keep track of the influence of $\kappa$ in all error contri- butions. ... mehr


Volltext §
DOI: 10.5445/IR/1000174322
Veröffentlicht am 19.09.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 09.2024
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000174322
Verlag KIT, Karlsruhe
Umfang 39 S.
Serie CRC 1173 Preprint ; 2024/21
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Externe Relationen Forschungsdaten/Software
Abstract/Volltext
Schlagwörter Ginzburg–Landau equation, superconductivity, error analysis, finite element method
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page