Convergence rate for the method Of moments with linear closure relations

Yves Bourgault; Damien Broizat; Pierre Emmanuel Jabin

doi:10.3934/krm.2015.8.1

Convergence rate for the method Of moments with linear closure relations

Yves Bourgault, Damien Broizat, Pierre Emmanuel Jabin

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplied, 1 dimensional setting, we are able to prove stability estimates for the method (with a kinetic interpretation by a BGK model). Moreover we are also able to obtain convergence rates which automatically increase with the smoothness of the initial data.

Original language	English (US)
Pages (from-to)	1-27
Number of pages	27
Journal	Kinetic and Related Models
Volume	8
Issue number	1
DOIs	https://doi.org/10.3934/krm.2015.8.1
State	Published - 2015

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation

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abstract = "We study linear closure relations for the moments' method applied to simple kinetic equations. The equations are linear collisional models (velocity jump processes) which are well suited to this type of approximation. In this simplied, 1 dimensional setting, we are able to prove stability estimates for the method (with a kinetic interpretation by a BGK model). Moreover we are also able to obtain convergence rates which automatically increase with the smoothness of the initial data.",

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