Equivalence between the Energy Stable Flux Reconstruction and Filtered Discontinuous Galerkin Schemes: Numerical Validation
Bibliographic record
Abstract
The aim of this paper is to numerically demonstrate the equivalence between filtered Discontinuous Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes in the general context of higher dimensional curvilinear element formulations. We first present the theory, as outlined in our previous work, demonstrating that all ESFR scheme correction fields can be interpreted as modally filtered DG correction fields in the strong form of the schemes, and further, that ESFR schemes can be interpreted as a DG scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction. The theoretical derivations are then verified with numerical results obtained for a 3D Euler test case with curved geometry on both tetrahedral and hexahedral meshes. Given the current choice of high-order DG-type schemes and the question as to which might be best to use for a specific application, the main significance of this work is the bridge that it provides between them. Clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use ESFR schemes, as opposed to the weak DG scheme, when solving problems implicitly.
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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 | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".