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Titlebook: Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws; Philipp Öffner Book 2023 The Editor(s) (if a

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发表于 2025-3-21 18:03:42 | 显示全部楼层 |阅读模式
期刊全称Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws
影响因子2023Philipp Öffner
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图书封面Titlebook: Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws;  Philipp Öffner Book 2023 The Editor(s) (if a
影响因子The book focuses on stability and approximation results concerning recent numerical methods for the numerical solution of hyperbolic conservation laws. The work begins with a detailed and thorough introduction of hyperbolic conservation/balance laws and their numerical treatment. In the main part, recent results in such context are presented focusing on the investigation of approximation properties of discontinuous Galerkin and flux reconstruction methods, the construction of (entropy) stable numerical methods and the extension of existing (entropy) stability results for both semidiscrete and fully discrete schemes, and development of new high-order methods..
Pindex Book 2023
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Uncertainty Quantification for Burgers’ Equationdata and, in general, one distinguishes between numerical errors which we already investigated and these uncertainties. The errors are strictly deterministic quantities, whereas the uncertainties are stochastic quantities.
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Analysis, Re-interpretation and Extension of Entropy Correction Terms. In this following part, we focus on these correction terms and their suggested modification as presented in [267] deeper. We characterize them as solutions of certain optimization problems and adapt them to the SBP-SAT framework including discontinuous Galerkin and (multi-block) finite difference
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Arbitrary High-order, Conservative and Positivity Preserving Patankar-type Deferred Correction Schem Chapter 6, the applied time integration method has also a big influence on the performance of the fully discrete scheme. Therefore, classical time integrations methods like RK and DeC have to be studied with respect to the desired properties.
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Summary & Outlookular, I have presented novel results concerning approximation and stability properties of several high-order schemes and have constructed new methods with desirable properties for both conservation laws and production – destruction systems. With the progress made here, I was able to close some gaps
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