MétaCan
Menu
Back to cohort
Record W3190448778

Finite element approximation of steady flows of colloidal solutions

2021· article· en· W3190448778 on OpenAlex
Κ. R. Rajagopal

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueOxford University Research Archive (ORA) (University of Oxford) · 2021
Typearticle
Languageen
FieldEngineering
TopicAdvanced Numerical Methods in Computational Mathematics
Canadian institutionsUniversity of Ottawa
FundersNational Science Foundation
KeywordsMathematicsFinite element methodMixed finite element methodMathematical analysisLipschitz continuityNonlinear systemDiscretizationExtended finite element methodPartial differential equationUniquenessWeak formulationApplied mathematicsBoundary value problemPhysics
DOInot available

Abstract

fetched live from OpenAlex

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.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.274
Threshold uncertainty score0.817

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.050
GPT teacher head0.288
Teacher spread0.238 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it