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

Willem Hundsdorfer; David I. Ketcheson; Igor Savostianov

doi:10.1007/s10915-014-9906-1

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

Willem Hundsdorfer, David I. Ketcheson, Igor Savostianov

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English (US)
Pages (from-to)	633-653
Number of pages	21
Journal	Journal of Scientific Computing
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s10915-014-9906-1
State	Published - Aug 27 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): FIC/2010/05
Acknowledgements: This work has been supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).

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10.1007/s10915-014-9906-1

https://repository.kaust.edu.sa/bitstream/10754/333609/1/2014_partitioned_multirate_postprint.pdf

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title = "Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws",

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.",

author = "Willem Hundsdorfer and Ketcheson, {David I.} and Igor Savostianov",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): FIC/2010/05 Acknowledgements: This work has been supported by Award No. FIC/2010/05 from King Abdullah University of Science and Technology (KAUST).",

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AU - Ketcheson, David I.

AU - Savostianov, Igor

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N2 - 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.

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

Abstract

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