Development of Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients
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Bibliographic record
Abstract
The generalized summation-by-parts (GSBP) framework enables the derivation of novel and potentially efficient provably stable high-order finite-difference operators, applicable on general nodal distributions. This paper explores the application of GSBP operators to the solution of partial differential equations with firstand second-derivative terms. Here, we investigate compatible and order-matched GSBP operators for the approximation of the second derivative with a variable coefficient. These operators are one order more accurate than the application of the first-derivative operator twice and more dissipative of underresolved modes. Several example operators are described in detail. To characterize the various operators, the steady linear convection-diffusion equation with a variable coefficient is solved.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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