Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertainties

DOI10.1137/24m1638483zbMath1547.65159MaRDI QIDQ6587626

Kunlun Qi, Liu Liu

Publication date: 14 August 2024

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

zbMATH Keywords

Boltzmann equationFourier-Galerkin spectral methoduncertainty quantificationconvergence and stabilitygPC-based stochastic Galerkin methodsemi-discretized numerical system

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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Boltzmann equations (35Q20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions
• Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation
• Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings
• Kinetic description of optimal control problems and applications to opinion consensus
• Mathematical modeling of collective behavior in socio-economic and life sciences
• Uncertainty quantification for systems of conservation laws
• The Boltzmann equation and its applications
• Uncertainty quantification for hyperbolic and kinetic equations
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• Modeling and computational methods for kinetic equations
• Hypocoercivity of stochastic Galerkin formulations for stabilization of kinetic equations
• A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
• Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case
• A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation
• Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel
• Polynomial chaos methods for hyperbolic partial differential equations. Numerical techniques for fluid dynamics problems in the presence of uncertainties
• A stochastic Galerkin method for the Boltzmann equation with uncertainty
• On the stability of spectral methods for the homogeneous Boltzmann equation
• An introduction to Monte Carlo method for the Boltzmann equation
• Analysis of spectral methods for the homogeneous Boltzmann equation
• A Fourier spectral method for homogeneous boltzmann equations
• A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases
• Fast algorithms for computing the Boltzmann collision operator
• Spectral Methods for Uncertainty Quantification
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Kinetic Derivation of Macroscopic Anticipation Models for Vehicular Traffic
• Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator
• Convergence and Error Estimates for the Lagrangian-Based Conservative Spectral Method for Boltzmann Equations
• Rigorous Analysis for Efficient Statistically Accurate Algorithms for Solving Fokker--Planck Equations in Large Dimensions
• Uniform Regularity for Linear Kinetic Equations with Random Input Based on Hypocoercivity
• Stochastic Numerics for the Boltzmann Equation
• Numerical methods for kinetic equations
• Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Uncertainty Quantification for the BGK Model of the Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods
• MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR MULTISCALE KINETIC EQUATIONS WITH UNCERTAINTIES
• A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels
• Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation
• A New Stability and Convergence Proof of the Fourier--Galerkin Spectral Method for the Spatially Homogeneous Boltzmann Equation
• Moment Preserving Fourier–Galerkin Spectral Methods and Application to the Boltzmann Equation
• A Positive and Moment-Preserving Fourier Spectral Method

This page was built for publication: Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertainties