TY - JOUR
T1 - ANALYSIS OF GALERKIN FEMS FOR MIXED FORMULATION OF TIME-DEPENDENT GINZBURG–LANDAU EQUATIONS UNDER TEMPORAL GAUGE
AU - WU, Chengda
AU - SUN, Weiwei
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Galerkin FEMs
KW - Ginzburg–Landau equations
KW - Nonclassical Ritz projection
KW - Optimal error estimate
KW - Temporal gauge
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U2 - 10.1137/17M113544X
DO - 10.1137/17M113544X
M3 - RGC 21 - Publication in refereed journal
VL - 56
SP - 1291
EP - 1312
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
SN - 0036-1429
IS - 3
ER -