ANALYSIS OF GALERKIN FEMS FOR MIXED FORMULATION OF TIME-DEPENDENT GINZBURG–LANDAU EQUATIONS UNDER TEMPORAL GAUGE

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Original languageEnglish
Pages (from-to)1291–1312
Journal / PublicationSIAM Journal on Numerical Analysis
Volume56
Issue number3
Online published15 May 2018
Publication statusPublished - 2018

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  • © 2018 Society for Industrial and Applied Mathematics.
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-85049443735&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(af36cbd8-ef1c-4b17-aeb0-d08f0105ee08).html

Abstract

The paper focuses on analysis of linearized Galerkin FEMs for a mixed formulation of the time-dependent Ginzburg–Landau equations under the temporal gauge. We provide optimal error estimates in L2 -norm for the order parameter ψh and the magnetic field σh  unconditionally, although the accuracy of the numerical magnetic potential Ah is one-order lower than the optimal one due to the degeneracy of the magnetic potential equation. Since the states of superconductors are determined by the order parameter ψh (or the density of the superconducting electron pairs |ψh|), the accuracy of ψh is more important for the vortex simulation in superconditors. Our analysis is based on a nonclassical Ritz projection, which may reduce the pollution of inaccuracy of the numerical magnetic potential in analysis. Numerical experiments confirm our theoretical analysis.

Research Area(s)

  • Galerkin FEMs, Ginzburg–Landau equations, Nonclassical Ritz projection, Optimal error estimate, Temporal gauge

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100
Order Mathematics
100
equations INIS
100
time dependence INIS
100
Density Material Science
100
Paper Material Science
100
Superconducting Mat... Material Science
100
Vortex Material Science
100
Parameter Physics
100
Formulation Earth and Planetary Scien...
100
Gauge Earth and Planetary Scien...
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[ RIS ] [ BibTeX ]
ANALYSIS OF GALERKIN FEMS FOR MIXED FORMULATION OF TIME-DEPENDENT GINZBURG–LANDAU EQUATIONS UNDER TEMPORAL GAUGE. / WU, Chengda; SUN, Weiwei.
In: SIAM Journal on Numerical Analysis, Vol. 56, No. 3, 2018, p. 1291–1312.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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