Fictitious domain method: A stabilized post-processing technique for boundary-flux calculation using cut elements
Bibliographic record
Abstract
This paper presents a technique for calculating boundary fluxes in the context of fictitious domain methods. We focus on a simple boundary-value problem and use Nitsche’s method stabilized with ghost penalty for the finite element formulation. To recover the flux, we derive a formulation directly from the boundary-value problem’s finite element formulation. Since the boundary may not align with the mesh, we compute the approximate flux using piecewise linear polynomials on cut elements. We then deduce the desired flux as the trace of the solution on the boundary. To ensure that the condition number of the resulting system matrix is independent of the boundary’s position on the mesh, we add a ghost penalty term. This term acts on the jumps of the gradients over interior facets belonging to elements intersected by the boundary. Two and three-dimensional numerical examples are provided, and show that the method is accurate and has optimal convergence regardless of the immersed boundary position.
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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 | 0.002 |
| 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 | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".