scholarly journals Dynamical Low-Rank Integrator for the Linear Boltzmann Equation: Error Analysis in the Diffusion Limit

2021 ◽  
Vol 59 (4) ◽  
pp. 2254-2285
Author(s):  
Zhiyan Ding ◽  
Lukas Einkemmer ◽  
Qin Li
Keyword(s):  
Boltzmann Equation ◽  
Error Analysis ◽  
Low Rank ◽  
Linear Boltzmann Equation ◽  
Diffusion Limit ◽  
Equation Error

Anomalous diffusion limit for a linear Boltzmann equation with external force field

2017 ◽  
Vol 27 (05) ◽  
pp. 845-878 ◽  
Author(s):  
Pedro Aceves-Sanchez ◽  
Antoine Mellet
Keyword(s):  
Boltzmann Equation ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Linear Boltzmann Equation ◽  
Diffusion Limit ◽  
Acceleration Field ◽  
Fractional Diffusion Equations ◽  
External Force Field ◽  
Advection Term ◽  
External Acceleration

This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to investigate the case where a given acceleration field is present. The main result of this paper shows that for an appropriate scaling of the acceleration field, the usual fractional diffusion equation is supplemented by an advection term. Both the critical and supercritical case are considered.

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