<i>H</i><sup>1</sup>‐superconvergence of finite difference method based on <i>Q</i><sub>1</sub>‐element on quasi‐uniform mesh for the 3D Poisson equation
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Bibliographic record
Abstract
Abstract In this paper, the finite difference (FD) method is considered for the 3D Poisson equation by using the Q 1 ‐element on a quasi‐uniform mesh. First, under the regularity assumption of , the H 1 ‐superconvergence of the FD solution u h based on the Q 1 ‐element to the first‐order interpolation function is obtained. Next, the H 1 ‐superconvergence of the second‐order interpolation postprocessing function based on the FD solution u h to u is provided. Finally, numerical tests are presented to show the H 1 ‐superconvergence result of the FD postprocessing function to u if .
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| 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