# American Institute of Mathematical Sciences

March  2015, 8(1): 1-27. doi: 10.3934/krm.2015.8.1

## Convergence rate for the method of moments with linear closure relations

 1 Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, Ontario, Canada 2 Laboratoire J.-A. Dieudonné, Université de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France 3 CSCAMM and Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States

Received  October 2014 Revised  October 2014 Published  December 2014

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.
Citation: Yves Bourgault, Damien Broizat, Pierre-Emmanuel Jabin. Convergence rate for the method of moments with linear closure relations. Kinetic & Related Models, 2015, 8 (1) : 1-27. doi: 10.3934/krm.2015.8.1
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