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

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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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Acknowledgments

This paper originated from work of W. H. with Anna Mozartova and Valeriu Savcenco. The contributions of Mozartova and Savcenco, on the design of multirate methods and monotonicity properties of these methods, are contained in [6]. They are thanked for helpful comments on preliminary convergence results for first-order methods.

Author information

Correspondence to Willem Hundsdorfer.

Additional information

This work has been supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).

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

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Keywords

  • Multirate methods
  • Partitioned Runge–Kutta methods
  • Conservation
  • Stability
  • Convergence

Mathematics Subject Classification

  • 65L06
  • 65M06
  • 65M20