Convergence rate for the method of moments with linear closure relations

TL;DR

This paper analyzes the convergence rates of the method of moments with linear closure for simple kinetic equations, providing stability estimates and showing that convergence improves with initial data smoothness.

Contribution

It offers the first stability and convergence rate analysis for the method of moments with linear closure in a kinetic setting.

Findings

Proves stability estimates for the method.

Shows convergence rates increase with initial data smoothness.

Provides a kinetic interpretation via a BGK model.

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 simplified, 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.