Paper Info
Title
Analysis of Galerkin FEMs for Mixed Formulation of Time-Dependent Ginzburg--Landau Equations Under Temporal Gauge
Abstract
AbstractThe paper focuses on analysis of linearized Galerkin FEMs for a mixed formulation ofthe time-dependent Ginzburg--Landau equations under the temporal gauge. We provideoptimal error estimates in $L^2$-norm for the order parameter $\psi_h$ and the magneticfield $\sigma_h$ unconditionally, although the accuracy of the numerical magnetic potential$\mathbf{A}_h$ is one-order lower than the optimal one due to the degeneracy of the magneticpotential equation. Since the states of superconductors are determined by the order parameter$\psi_h$ (or the density of the superconducting electron pairs $|\psi_h|$), the accuracy of$\psi_h$ is more important for the vortex simulation in superconditors. Our analysis is basedon a nonclassical Ritz projection, which may reduce the pollution of inaccuracy of thenumerical magnetic potential in analysis. Numerical experiments confirm our theoretical analysis.
Year
DOI
Venue
2018
10.1137/17M113544X
Periodicals
Keywords
Field
DocType
nonclassical Ritz projection,Ginzburg-Landau equations,Galerkin FEMs,temporal gauge,optimal error estimate
Magnetic field,Superconductivity,Mathematical analysis,Galerkin method,Vortex,Electron pair,Degeneracy (mathematics),Magnetic potential,Gauge (firearms),Mathematics
Journal
Volume
Issue
ISSN
56
3
0036-1429
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Chengda Wu100.34
Weiwei Sun215415.12