A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation

DOI10.1137/20M1351813zbMath1462.35235arXiv2007.05184OpenAlexW3135290219MaRDI QIDQ5855634

No author found.

Publication date: 19 March 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.05184

zbMATH Keywords

stabilityconvergencewell-posednessBoltzmann equationFourier-Galerkin spectral methodfilterdiscontinuous

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20)

Related Items (6)

Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation ⋮ A Fast Petrov--Galerkin Spectral Method for the Multidimensional Boltzmann Equation Using Mapped Chebyshev Functions ⋮ Representation theory based algorithm to compute Boltzmann's bilinear collision operator in the irreducible spectral Burnett ansatz efficiently ⋮ A Positive and Moment-Preserving Fourier Spectral Method ⋮ On the measure valued solution to the inelastic Boltzmann equation with soft potentials ⋮ Global existence and stability of solutions of spatially homogeneous Boltzmann equation for Fermi-Dirac particles

Uses Software

• Boltzmann

Cites Work

• Unnamed Item
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