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.
| Original language | English |
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| Pages (from-to) | 1291–1312 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 56 |
| Issue number | 3 |
| Online published | 15 May 2018 |
| DOIs | |
| Publication status | Published - 2018 |
Research Keywords
- Galerkin FEMs
- Ginzburg–Landau equations
- Nonclassical Ritz projection
- Optimal error estimate
- Temporal gauge
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2018 Society for Industrial and Applied Mathematics.