Finite Element Method for Internal Wave Equation for Stratified Fluid
Bibliographic record
Abstract
In many areas of natural science non-stationary problems on internal wave motion arise. For example, such problems appear in aerophysics, geophysics, oceanology, in theory of rotating fluid, and at design and construction of mining constructions (Gabov & Sveshnikov, 1990). It is a complicated mathematical problem to obtain accurate analytical solutions for such problems. In such cases a natural apparatus for study of internal wave motion processes is in numerical methods. In this work, the schemes of the finite element method with high accuracy in space and time for solution of a mixed boundary problem for internal wave equation for stratified fluid are proposed and studied. The schemes constructed have specific advantages compared to the other schemes: a scheme with high order of accuracy (more than two); besides the solution itself one finds along which that its derivative (velocity) with the same accuracy; at use of interpolation representation of the solution one can obtain, if needed, the solution and its derivative for an arbitrary instant; since the schemes are two-layer ones, one can use variable step without loss of accuracy; the scheme is conventionally stable and requires 4 times more arithmetical operations compared to ordinary ones, though this scheme makes it possible to choose larger time steps to get given accuracy. Besides that, evaluations of accuracy of the schemes for the problem under consideration are obtained. By means of dispersion analysis comparison to known schemes is carried out.
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How this classification was reachedexpand
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 | 0.000 |
| 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 | 0.002 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".