𝐻¹-Superconvergence of a difference finite element method based on the 𝑃₁-𝑃₁-conforming element on non-uniform meshes for the 3D Poisson equation
Bibliographic record
Abstract
In this paper, a difference finite element (DFE) method is presented for the 3D Poisson equation on non-uniform meshes by using the P 1 − P 1 P_1-P_1 -conforming element. This new method consists of combining the finite difference discretization based on the P 1 P_1 -element in the z z -direction with the finite element discretization based on the P 1 P_1 -element in the ( x , y ) (x,y) -plane. First, under the regularity assumption of u ∈ H 3 ( Ω ) ∩ H 0 1 ( Ω ) u\in H^3(\Omega )\cap H^1_0(\Omega ) and ∂ z z f ∈ L 2 ( ( 0 , L 3 ) ; \partial _{zz}f\in L^2((0, L_3); H − 1 ( ω ) ) H^{-1}(\omega )) , the H 1 H^1 -superconvergence of the discrete solution
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".