TY  - JOUR
AU  - Breuß, Michael
AU  - Kleefeld, Andreas
TI  - Implicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms
JO  - Acta mathematica Vietnamica
VL  - 45
IS  - 3
SN  - 0251-4184
CY  - Singapore
PB  - Springer Singapore
M1  - FZJ-2020-00128
SP  - 709–738
PY  - 2020
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000565039800009
DO  - DOI:10.1007/s40306-019-00354-1
UR  - https://juser.fz-juelich.de/record/872637
ER  -