The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized entropy-based moment method was recently introduced to remove one of the main challenges in the implementation of the entropy-based moment method, namely the requirement of the realizability of the numerical solution. In this work we use the method of relative entropy to prove the convergence of the regularized method to the original method as the regularization parameter goes to zero and give convergence rates. Our main assumptions are the boundedness of the velocity domain and that the original moment solution is Lipschitz continuous in space and bounded away from the boundary of realizability. We provide results from numerical simulations showing that the convergence rates we prove are optimal.
DOI: 10.5802/smai-jcm.93
Graham W. Alldredge 1; Martin Frank 2; Jan Giesselmann 3
CC-BY 4.0
@article{SMAI-JCM_2023__9__1_0,
author = {Graham W. Alldredge and Martin Frank and Jan Giesselmann},
title = {On the convergence of the regularized entropy-based moment method for kinetic equations},
journal = {The SMAI Journal of computational mathematics},
pages = {1--29},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {9},
year = {2023},
doi = {10.5802/smai-jcm.93},
zbl = {07650810},
mrnumber = {4573690},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.93/}
}
TY - JOUR AU - Graham W. Alldredge AU - Martin Frank AU - Jan Giesselmann TI - On the convergence of the regularized entropy-based moment method for kinetic equations JO - The SMAI Journal of computational mathematics PY - 2023 SP - 1 EP - 29 VL - 9 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.93/ DO - 10.5802/smai-jcm.93 LA - en ID - SMAI-JCM_2023__9__1_0 ER -
%0 Journal Article %A Graham W. Alldredge %A Martin Frank %A Jan Giesselmann %T On the convergence of the regularized entropy-based moment method for kinetic equations %J The SMAI Journal of computational mathematics %D 2023 %P 1-29 %V 9 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.93/ %R 10.5802/smai-jcm.93 %G en %F SMAI-JCM_2023__9__1_0
Graham W. Alldredge; Martin Frank; Jan Giesselmann. On the convergence of the regularized entropy-based moment method for kinetic equations. The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 1-29. doi : 10.5802/smai-jcm.93. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.93/
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