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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes
verfasst von : Willem Hundsdorfer, Anna Mozartova, Valeriu Savcenco
Erschienen in: Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws
Verlag: Springer Berlin Heidelberg
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Multirate schemes for conservation laws or convection-dominated problems seem to come in two flavors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods.