Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes
KAUST Grant NumberFIC/2010/05
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AbstractMultirate 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.
CitationHundsdorfer W, Mozartova A, Savcenco V (2013) Monotonicity Conditions for Multirate and Partitioned Explicit Runge-Kutta Schemes. Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws: 177–195. Available: http://dx.doi.org/10.1007/978-3-642-33221-0_11.
SponsorsThe work of W. Hundsdorfer is supported by Award No. FIC/2010/05from King Abdullah University of Science and Technology (KAUST). The work ofA. Mozartova has been supported by a grant from the Netherlands Organisation for ScientificResearch NWO.
PublisherSpringer Science + Business Media