Abstract
Induced numerical oscillations in the computed solution by monotone schemes for hyperbolic conservation laws has been a focus of recent studies. In this work using a local maximum principle, the monotone stable Lax-Friedrichs (LxF) scheme is investigated to explore the cause of induced local oscillations in the computed solution. It expounds upon that LxF scheme is locally unstable and therefore exhibits induced such oscillations. The carried out analysis gives a deeper insight to characterize the type of data extrema and the solution region which cause local oscillations. Numerical results for benchmark problems are also given to support the theoretical claims.
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