Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit

From MaRDI portal
Publication:2999843

DOI10.1137/090772770zbMath1220.65116arXiv0910.0518OpenAlexW1967154621MaRDI QIDQ2999843

Jian-Guo Liu, Luc Mieussens

Publication date: 17 May 2011

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

Full work available at URL: https://arxiv.org/abs/0910.0518



Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).


Related Items (35)

A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantificationAsymptotic-preserving schemes for multiscale physical problemsIdentification of the diffusion parameter in nonlocal steady diffusion problemsAn asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equationA unified gas-kinetic scheme for continuum and rarefied flows. IV: Full Boltzmann and model equationsThe fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operatorAsymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limitAsymptotic preserving schemes for highly oscillatory Vlasov-Poisson equationsOn the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic modelsUniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving methodAn asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalingsAsymptotic-preserving methods and multiscale models for plasma physicsAsymptotic Preserving and Uniformly Unconditionally Stable Finite Difference Schemes for Kinetic Transport EquationsOn a discrete framework of hypocoercivity for kinetic equationsHybrid kinetic/fluid numerical method for the Vlasov-BGK equation in the diffusive scalingStability-enhanced AP IMEX-LDG schemes for linear kinetic transport equations under a diffusive scalingAsymptotic-Preserving and Energy Stable Dynamical Low-Rank ApproximationProof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshesMicro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equationsInterface problems in nonlocal diffusion and sharp transitions between local and nonlocal domainsOn the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equationsAsymptotic Preserving Error Estimates for Numerical Solutions of Compressible Navier--Stokes Equations in the Low Mach Number RegimeExistence and uniqueness of weak solutions for nonlocal parabolic problems via the Galerkin methodFast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applicationsAsymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn EquationsAn Asymptotic Preserving Two-dimensional Staggered Grid Method for Multiscale Transport EquationsHigh order asymptotic preserving DG-IMEX schemes for discrete-velocity kinetic equations in a diffusive scalingA spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditionsUniform convergence of an upwind discontinuous Galerkin method for solving scaled discrete-ordinate radiative transfer equations with isotropic scatteringMultiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order SchemesHypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equationsNonlocal convection-diffusion problems on bounded domains and finite-range jump processesA Positive Asymptotic-Preserving Scheme for Linear Kinetic Transport EquationsStability-enhanced AP IMEX1-LDG Method: Energy-based Stability and Rigorous AP PropertyAnalysis of an Asymptotic Preserving Scheme for Stochastic Linear Kinetic Equations in the Diffusion Limit




This page was built for publication: Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit