{\em A POSTERIORI} ERROR ESTIMATION FOR A DUAL MIXED FINITE ELEMENT METHOD FOR QUASI--NEWTONIAN FLOWS WHOSE VISCOSITY OBEYS A POWER LAW OR CARREAU LAW
Bibliographic record
Abstract
A dual mixed finite element method, for quasi-Newtonian fluid flow obeying the power law or the Carreau law, is constructed and analyzed in Farhloul-Zine [13].This mixed formulation possesses good local (i.e., at element level) conservation properties (conservation of the momentum and the mass) as in the finite volume methods.In Farhloul-Zine [12], we developed an a posteriori error analysis for a non-Newtonian fluid flow problems.The analysis is based on the fact that the equation describing the extra-stress tensor in terms of the rate of strain tensor is invertible and may give the rate of strain tensor as a function of the stress tensor.To free ourselves from this constraint of inversion of laws, and as a generalization of the obtained results in [12], we propose in this work an a posteriori error analysis to this mixed formulation.
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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 | 0.002 | 0.005 |
| 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".