A new polynomial reconstruction scheme AENO-C for ADER methods to very-high orders of accuracy
Bibliographic record
Abstract
In this paper, we introduce AENO-C, a high-order polynomial reconstruction scheme that builds upon AENO by employing a special averaging of the ENO polynomial and a conservative polynomial constructed from the centred stencil closest to the ENO stencil, using a new joining function with improved asymptotic properties. The scheme is systematically evaluated within the ADER finite-volume framework up to tenth-order accuracy on test cases involving the linear advection equation, Burgers’ equation with a source term, and the Euler equations. It is found to perform highly satisfactorily across different scenarios, including both smooth and discontinuous profiles, and for all considered orders of accuracy. For smooth solutions, it exhibits convergence rates clearly superior to ENO and the original AENO, making it competitive and, in many situations, even more efficient than WENO in achieving a given error tolerance. For discontinuous solutions, it demonstrates remarkable robustness, effectively resolving complex features with high fidelity while preventing the appearance of spurious oscillations. The new reconstruction scheme is simple to implement, computationally cheap, with a cost comparable to ENO and AENO, and provides a closed form polynomial expression which can be evaluated at any desired point.
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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 | 0.000 |
| 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 | 0.002 |
| 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".