Mixed finite element method in 3D for a nonlinear eddy current problem
Bibliographic record
Abstract
The purpose of this paper is to demonstrate the convergence of a mixed finite element formulation in 3D for a nonlinear eddy current problem encountered in the modelling of Type II superconductors. The eddy current problem models the magnetic field in a material with a power law magnetic resistivity which makes it an analogue of the p-Laplacian. Yet in contrast to the p-Laplacian, the resulting time-transient degenerate parabolic problem includes a divergence constraint and requires non-conforming elements. Numerical discretizations of this problem, sometimes referred to as the p-curl, have been studied by many, but the well-posedness of mixed formulations has only been established in 2D by Prigozhin and Barrett. This research extends earlier work of Farhloul on the p-Laplacian and discusses well-posedness both for the continuous and the discrete formulation using first-order Nédélec elements.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".