Error estimate of energy stable flux reconstruction methods
Bibliographic record
Abstract
Energy stable flux reconstruction is a high-order numerical method used for solving partial differential equations in computational fluid dynamics. This method is designed to preserve the energy stability of the underlying partial differential equation system with respect to a broken Sobolev norm. This property makes this method particularly suitable for simulating problems that involve strong shocks or discontinuities. First a class of one-parameter schemes has been identified to be stable for the one-dimensional linear advection equation by Vincent, Castonguay and Jameson in 2011. This class includes some well-known high order methods such as the discontinuous Galerkin method and spectral difference method. The main advantage of the energy stable flux reconstruction is to allow for an increase in the maximum admissible time step while retaining the stability and accuracy properties of the underlying scheme. However numerical experiments have shown that beyond a certain value of the parameter, optimal order of accuracy is lost. This work introduces an L-error estimate for energy stable flux reconstruction scheme applied to the one-dimensional advection equation following the outlines of Cockburn's proof for discontinuous Galerkin method.
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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 | 0.006 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".