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On the convergence of the regularized entropy-based moment method for kinetic equations

Alldredge, Graham W.; Frank, Martin 1; Giesselmann, Jan
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)


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.

Volltext §
DOI: 10.5445/IR/1000156982
Veröffentlicht am 16.03.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2021
Sprache Englisch
Identifikator KITopen-ID: 1000156982
Umfang 32 S.
Vorab online veröffentlicht am 21.05.2021
Nachgewiesen in Dimensions
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