Journal of Scientific Computing

, Volume 75, Issue 2, pp 1057–1078 | Cite as

Strong Stability Preserving Explicit Peer Methods for Discontinuous Galerkin Discretizations

Article
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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.

Keywords

Discontinuous Galerkin Strong stability preserving Explicit peer methods 

Mathematics Subject Classification

65L05 65L06 
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Notes

Acknowledgements

The authors are grateful to the anonymous referees for their valuable remarks and comments on the paper.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Institute of MathematicsMartin Luther University Halle-WittenbergHalle (Saale)Germany

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