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000872637 1001_ $$0P:(DE-HGF)0$$aBreuß, Michael$$b0
000872637 245__ $$aImplicit Monotone Difference Methods for Scalar Conservation Laws with Source Terms
000872637 260__ $$aSingapore$$bSpringer Singapore$$c2020
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000872637 520__ $$aIn 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.
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000872637 7001_ $$0P:(DE-Juel1)169421$$aKleefeld, Andreas$$b1$$eCorresponding author
000872637 773__ $$0PERI:(DE-600)2620691-2$$a10.1007/s40306-019-00354-1$$gVol. 45, no. 3, p. 709 - 738$$n3$$p709–738$$tActa mathematica Vietnamica$$v45$$x0251-4184$$y2020
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