A locally conservative and energy‐stable finite‐element method for the Navier‐Stokes problem on time‐dependent domains
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Bibliographic record
Abstract
Summary We present a finite‐element method for the incompressible Navier‐Stokes problem that is locally conservative, energy‐stable, and pressure‐robust on time‐dependent domains. To achieve this, the space‐time formulation of the Navier‐Stokes problem is considered. The space‐time domain is partitioned into space‐time slabs, which in turn are partitioned into space‐time simplices. A combined discontinuous Galerkin method across space‐time slabs and space‐time hybridized discontinuous Galerkin method within a space‐time slab results in an approximate velocity field that is H (div)‐conforming and exactly divergence‐free, even on time‐dependent domains. Numerical examples demonstrate the convergence properties and performance of the method.
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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 | 0.003 | 0.003 |
| 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 | 0.001 | 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 it