Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property

DOI10.1137/20M1336503zbMath1468.65147arXiv2005.05454OpenAlexW3151879920MaRDI QIDQ4986816

Fengyan Li, Yingda Cheng, Zhichao Peng, Jing-Mei Qiu

Publication date: 28 April 2021

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

Full work available at URL: https://arxiv.org/abs/2005.05454

zbMATH Keywords

numerical stabilitymultiscalediscontinuous Galerkinasymptotic preservingenergy approachkinetic transport equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for stiff equations (65L04)

Related Items (3)

Hyperbolic balance laws: modeling, analysis, and numerics. Abstracts from the workshop held February 28 -- March 6, 2021 (hybrid meeting) ⋮ High order asymptotic preserving discontinuous Galerkin methods for gray radiative transfer equations ⋮ Asymptotic Preserving and Uniformly Unconditionally Stable Finite Difference Schemes for Kinetic Transport Equations

Uses Software

• FV_HipoDiff

Cites Work

• Unnamed Item
• Numerical schemes for kinetic equations in diffusive regimes
• On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models
• An asymptotic preserving scheme based on a micro-macro decomposition for collisional Vlasov equations: diffusion and high-field scaling limits
• High order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scaling
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Stability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scaling
• Asymptotically complexity diminishing schemes (ACDS) for kinetic equations in the diffusive scaling
• Operator bounds and time step conditions for the DG and central DG methods
• Analysis of an Asymptotic Preserving Scheme for Relaxation Systems
• High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems
• Analysis of Asymptotic Preserving DG-IMEX Schemes for Linear Kinetic Transport Equations in a Diffusive Scaling
• Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit
• Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
• Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method
• An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
• Uniform Stability of a Finite Difference Scheme for Transport Equations in Diffusive Regimes
• Implicit-Explicit Runge--Kutta Schemes for Hyperbolic Systems and Kinetic Equations in the Diffusion Limit
• On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations
• A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit
• Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
• Analysis of an Asymptotic Preserving Scheme for Stochastic Linear Kinetic Equations in the Diffusion Limit
• Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

This page was built for publication: Stability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP Property