A robust goal-oriented estimator based on the construction of equilibrated fluxes for discontinuous Galerkin finite element approximations of convection-diffusion problems
Bibliographic record
Abstract
We propose an a posteriori error estimator with respect to quantities of interest for dis-continuous Galerkin approximations of convection-diffusion boundary-value problems. The error estimator is based on the construction of equilibrated fluxes in Raviart-Thomas finite element spaces and on the solution of the dual problem. We show that it is asymptotically exact in both the elliptic and hyperbolic regimes if the dual problem is approximated by a discontinuous Galerkin method of order one greater than that of the primal problem. We show in this case that the effectivity index behaves as (1+Pe 1/2)o(h), where Pe is the Péclet number and h the mesh diameter. It follows that the quality of the effectivity index may deteriorate for large values of Pe, but we put in evidence that it suffices to increase the approximation order of the dual problem to keep the effectivity index close to unity even on coarse meshes. Two-dimensional numerical examples demonstrate the robustness of the error estimator in both the diffusion and advection regimes.
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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 | 0.004 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".