Convergence of Spectral Discretizations of the Vlasov--Poisson System

DOI10.1137/16M1076848zbMath1375.65118arXiv1612.08013MaRDI QIDQ5363384

Daniele Funaro, Gianmarco Manzini, Gian Luca Delzanno

Publication date: 6 October 2017

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

Full work available at URL: https://arxiv.org/abs/1612.08013

zbMATH Keywords

stabilityconvergenceerror estimatesVlasov equationVlasov-Poisson systemLegendre spectral methodHermite spectral methodperiodic Fourier expansions

Mathematics Subject Classification ID

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Vlasov equations (35Q83)

Related Items (11)

On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system ⋮ A decision-making machine learning approach in Hermite spectral approximations of partial differential equations ⋮ Error analysis of Fourier–Legendre and Fourier–Hermite spectral-Galerkin methods for the Vlasov–Poisson system ⋮ The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations ⋮ Physics-based adaptivity of a spectral method for the Vlasov-Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space ⋮ On the Convergence of Discontinuous Galerkin/Hermite Spectral Methods for the Vlasov–Poisson System ⋮ Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov-Poisson system ⋮ A semi-Lagrangian spectral method for the Vlasov-Poisson system based on Fourier, Legendre and Hermite polynomials ⋮ A generalized Fourier-Hermite method for the Vlasov-Poisson system ⋮ Stability and conservation properties of Hermite-based approximations of the Vlasov-Poisson system ⋮ On the use of Hermite functions for the Vlasov-Poisson system

Uses Software

• Viriato
• SpectralPlasmaSolver

Cites Work

• On the velocity space discretization for the Vlasov-Poisson system: comparison between implicit Hermite spectral and particle-in-cell methods
• Convergence of Galerkin approximation for two-dimensional Vlasov-Poisson equation
• Viriato: a Fourier-Hermite spectral code for strongly magnetized fluid-kinetic plasma dynamics
• Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form
• A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system
• A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
• Spectral Methods
• Approximation Results for Orthogonal Polynomials in Sobolev Spaces
• A New Dual-Petrov-Galerkin Method for Third and Higher Odd-Order Differential Equations: Application to the KDV Equation
• Spectral velocity discretizations for the Vlasov-Maxwell equations
• Spectral Methods
• Conservative numerical schemes for the Vlasov equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Convergence of Spectral Discretizations of the Vlasov--Poisson System