Bibliographic record
Abstract
We consider the mathematical analysis and numerical approximation of a system\nof nonlinear partial differential equations that arises in models that have\nrelevance to steady isochoric flows of colloidal suspensions. The symmetric\nvelocity gradient is assumed to be a monotone nonlinear function of the\ndeviatoric part of the Cauchy stress tensor. We prove the existence of a unique\nweak solution to the problem, and under the additional assumption that the\nnonlinearity involved in the constitutive relation is Lipschitz continuous we\nalso prove uniqueness of the weak solution. We then construct mixed finite\nelement approximations of the system using both conforming and nonconforming\nfinite element spaces. For both of these we prove the convergence of the method\nto the unique weak solution of the problem, and in the case of the conforming\nmethod we provide a bound on the error between the analytical solution and its\nfinite element approximation in terms of the best approximation error from the\nfinite element spaces. We propose first a Lions-Mercier type iterative method\nand next a classical fixed-point algorithm to solve the finite-dimensional\nproblems resulting from the finite element discretisation of the system of\nnonlinear partial differential equations under consideration and present\nnumerical experiments that illustrate the practical performance of the proposed\nnumerical 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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".