Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws

2013/10/27 by Hundsdorfer, Willem, Ketcheson, David I., Savostianov, Igor
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1310.7168

Abstract

An error analysis is presented for explicit partitioned Runge-Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate.

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