Jean-Morlet Chair 2021- Workshop - Numerical Methods for Kinetic Equations (NumKin2021) / Chaire Jean-Morlet 2021 - Workshop - Méthodes numériques pour les équations cinétiques

Collection Jean-Morlet Chair 2021- Workshop - Numerical Methods for Kinetic Equations (NumKin2021) / Chaire Jean-Morlet 2021 - Workshop - Méthodes numériques pour les équations cinétiques

Organizer(s) Bostan, Mihaï ; Jin, Shi ; Mehrenberger, Michel

Date(s) 14/06/2021 - 18/06/2021

linked URL https://www.chairejeanmorlet.com/2356.html

00:00:00 / 00:00:00

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Stability of time discretizations for semi-discrete high order schemes for kinetic and related PDEs

By Chi-Wang Shu

When designing high order schemes for solving time-dependent kinetic and related PDEs, we often first develop semi-discrete schemes paying attention only to spatial discretizations and leaving time $t$ continuous. It is then important to have a high order time discretization to main the stability properties of the semi-discrete schemes. In this talk we discuss two classes of high order time discretization, i.e, the strong stability preserving (SSP) time discretization, which preserves strong stability from a stable spatial discretization with Euler forward, and the explicit Runge-Kutta methods, for which strong stability can be proved in many cases for semi-negative linear semi-discrete schemes. Numerical examples will be given to demonstrate the performance of these schemes.

Information about the video

Date of recording 11/05/2021
Date of publication 15/07/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19755603
Cite this video Shu, Chi-Wang (11/05/2021). Stability of time discretizations for semi-discrete high order schemes for kinetic and related PDEs. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19755603
URL https://dx.doi.org/10.24350/CIRM.V.19755603

Domain(s)

Numerical Analysis

Bibliography

SUN, Zheng et SHU, Chi-wang. Strong stability of explicit Runge--Kutta time discretizations. SIAM Journal on Numerical Analysis, 2019, vol. 57, no 3, p. 1158-1182. - https://arxiv.org/abs/1811.10680
XU, Yuan, ZHANG, Qiang, SHU, Chi-wang, et al. The L ^2-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations. SIAM Journal on Numerical Analysis, 2019, vol. 57, no 4, p. 1574-1601. - https://doi.org/10.1137/18M1230700

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