A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
Bibliographic record
Abstract
The method of characteristics type is especially effective for convection-dominated diffusion problems. Due to the nature of characteristic temporal discretization, the method allows one to use a large time step in many practical computations, while all previous theoretical analyses always required certain restrictions on the time stepsize. Here, we present a new analysis to establish unconditionally optimal error estimates for a modified method of characteristics with a mixed finite element approximation to the miscible displacement problem in $\mathbb{R}^d\ (d=2,3)$. For this purpose, we introduce a new characteristic time-discrete system. We prove that the $L^2$ error bound the characteristic time-discrete systemof the fully discrete method of characteristics to the time-discrete system is $\tau$-independent and the numerical solution is bounded in $W^{1,\infty}$-norm unconditionally. With the boundedness, optimal error estimates are established in a traditional manner. Numerical results confirm our theoretical analysis and clearly show the unconditional stability.
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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 | 0.004 |
| 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 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".