00:00:00 / 00:00:00

A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation

By Jingwei Hu

Appears in collection : Jean Morlet Chair 2021- Conference: Kinetic Equations: From Modeling Computation to Analysis / Chaire Jean-Morlet 2021 - Conférence : Equations cinétiques : Modélisation, Simulation et Analyse

Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourier-Galerkin spectral method has become a popular deterministic method for solving the Boltzmann equation, manifested by its high accuracy and potential of being further accelerated by the fast Fourier transform. Albeit its practical success, the stability of the method is only recently proved by Filbet, F. & Mouhot, C. in [Trans.Amer.Math.Soc. 363, no. 4 (2011): 1947-1980.] by utilizing the”spreading” property of the collision operator. In this work, we provide anew proof based on a careful L2 estimate of the negative part of the solution. We also discuss the applicability of the result to various initial data, including both continuous and discontinuous functions. This is joint work with Kunlun Qi and Tong Yang.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19734303
  • Cite this video Hu, Jingwei (22/03/2021). A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19734303
  • URL https://dx.doi.org/10.24350/CIRM.V.19734303

Bibliography

  • FILBET, Francis et MOUHOT, Clément. Analysis of spectral methods for the homogeneous Boltzmann equation. Transactions of the american mathematical society, 2011, vol. 363, no 4, p. 1947-1980. - http://dx.doi.org/10.1090/S0002-9947-2010-05303-6
  • HU, Jingwei, QI, Kunlun, et YANG, Tong. A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation. SIAM Journal on Numerical Analysis, 2021, vol. 59, no 2, p. 613-633. - https://doi.org/10.1137/20M1351813

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback