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Journal of Scientific Computing
Published in: Journal of Scientific Computing 2/2018

11-10-2017

Strong Stability Preserving Explicit Peer Methods for Discontinuous Galerkin Discretizations

Authors: Marcel Klinge, Rüdiger Weiner

Published in: Journal of Scientific Computing | Issue 2/2018

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Abstract

In this paper we study explicit peer methods with the strong stability preserving (SSP) property for the numerical solution of hyperbolic conservation laws in one space dimension. A system of ordinary differential equations is obtained by discontinuous Galerkin (DG) spatial discretizations, which are often used in the method of lines approach to solve hyperbolic differential equations. We present in this work the construction of explicit peer methods with stability regions that are designed for DG spatial discretizations and with large SSP coefficients. Methods of second- and third order with up to six stages are optimized with respect to both properties. The methods constructed are tested and compared with appropriate Runge–Kutta methods. The advantage of high stage order is verified numerically.
previous article Stability of Explicit Runge–Kutta Schemes
next article Guaranteed A Posteriori Error Estimates for a Staggered Discontinuous Galerkin Method

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Appendix
Available only for authorised users
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Metadata
Title
Strong Stability Preserving Explicit Peer Methods for Discontinuous Galerkin Discretizations
Authors
Marcel Klinge
Rüdiger Weiner
Publication date
11-10-2017
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 2/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0573-x

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