Investigation of the convergence of the mixed displacement-pressure formulation for three-dimensional poroelastic materials using hierarchical elements
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Bibliographic record
Abstract
Recently, a mixed pressure displacement [u, P] formulation based on Biot's poroelasticity equations has been presented for porous materials. This model leads to a reduction of the number of degrees of freedom required for the modeling of three-dimensional porous media in comparison to classical displacement-displacement [u, U] formulations. In this paper, an extension of the [u, P] formulation based on hierarchical elements is presented. First, a variant of the weak integral form of the [u, P] formulation is presented and its numerical implementation using hierarchical elements is detailed, together with the application of boundary and loading conditions. Numerical results are presented to show the accuracy and performance of the present approach. In particular, the importance of correctly capturing the coupling effects between the two phases is highlighted.
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Full frame distilled prediction
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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)
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 it