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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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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L. Heilmeyer,A. Schittenhelm,B. Rudderenty of various methods and studies in the literature cf. [135, 136, 305]. However, most of them are either based on finite difference (FD) or finite element approaches (FE), and we focus also here on these.

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https://doi.org/10.1007/978-3-662-33020-3data 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.

plasma

https://doi.org/10.1007/978-3-642-95087-2r, in the following chapter, we have an another topic in mind. In the DGSEM, the used quadrature rules have an enormous influence on the performance of the schemes, and, in general, Gauss-Lobatto or Gauss-Legendre quadratures are nowadays applied in the DGSEM by default.

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https://doi.org/10.1007/978-3-642-90616-9 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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Approximation and Stability Properties of Numerical Methods for Hyperbolic Conservation Laws