%0 Journal Article
%A Breuß, Michael
%A Kleefeld, Andreas
%T Implicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms
%J Acta mathematica Vietnamica
%V 45
%N 3
%@ 0251-4184
%C Singapore
%I Springer Singapore
%M FZJ-2020-00128
%P 709–738
%D 2020
%X In this article, a concept of implicit methods for scalar 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 monotonicity 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.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000565039800009
%R 10.1007/s40306-019-00354-1
%U https://juser.fz-juelich.de/record/872637