Analysis of Galerkin FEMs for Mixed Formulation of Time-Dependent Ginzburg--Landau Equations Under Temporal Gauge
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Bibliographic record
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 $L^2$-norm for the order parameter $\psi_h$ and the magnetic field $\sigma_h$ 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 magnetic potential 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 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.
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Full frame distilled prediction
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it