Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/100893
Title: Implicit monotone difference methods for scalar conservation laws with source terms
Authors: Breuß, Michael
Kleefeld, Andreas
Keywords: Conservation laws
Finite difference methods
Implicit methods
Monotone methods
Source term
Entropy solution
Issue Date: 2020
Series/Report no.: Acta mathematica Vietnamica journal;Vol.45, No.03 .- P.709-738
Abstract: In this article, a concept of implicit methods for sealar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970-986 2005). Implicit notions are developed that are centered around a mono- tonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
URI: https://dspace.ctu.edu.vn/jspui/handle/123456789/100893
ISSN: 0251-4184
Appears in Collections:Acta Mathematica Vietnamica 

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