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.
Multistep, Runge-Kutta and extrapolation methods (msc 65L06)
Null option (theme 11)
Journal of Scientific Computing
Multiscale Dynamics

Hundsdorfer, W, Ketcheson, D.I, & Savostianov, I. (2015). Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws. Journal of Scientific Computing, 63, 633–653. doi:10.1007/s10915-014-9906-1