Analysis of an SDG Method for the Incompressible Navier--Stokes Equations
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Bibliographic record
Abstract
In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier--Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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