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About the Lax‐Friedrichs scheme for the numerical approximation of hyperbolic conservation laws
Author(s) -
Breuß Michael
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410299
Subject(s) - conservation law , monotone polygon , simple (philosophy) , scheme (mathematics) , maxima and minima , mathematics , stability (learning theory) , numerical diffusion , diffusion , mathematical analysis , classical mechanics , physics , computer science , mechanics , geometry , quantum mechanics , philosophy , epistemology , machine learning
Abstract We discuss the numerical stability of the classical Lax‐Friedrichs method. The scheme features well‐established properties, especially it is TVD and monotone. However, it turns out that oscillations can occur at data extrema which seems to be in severe contrast to the large numerical diffusion the scheme exhibits. We briefly explain the phenomenon by use of a simple model problem and we give a short theoretical discussion. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)