Mixed Finite Element-Characteristic Mixed Finite Element Method for Simulating Three-Dimensional Incompressible Miscible Displacement Problems
Bibliographic record
Abstract
A mixed finite element with the characteristics is presented as a local conservative numerical approximation for an incompressible miscible problem in porous media. A mixed finite element (MFE) is used for the pressure and Darcy velocity, and a characteristic method is for the saturation. The convection term is discretized along the characteristic direction and the diffusion term is discretized by zero-order mixed finite element method. The method of characteristics confirms the strong stability without numerical dispersion at sharp fronts. Moreover, large time step is possibly adopted without any accuracy loss. The scalar unknown function and the adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux. In order to derive the optimal $3/2$-order error estimate in $L^2$ norm, a post-processing technique is included in the approximation to the scalar unknown saturation. This method can be used to solve the complicated problem.
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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 | 0.001 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".