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Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems

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Abstract

We examine the long time error behavior of discontinuous Galerkin spectral element approximations to hyperbolic equations. We show that the choice of numerical flux at interior element boundaries affects the growth rate and asymptotic value of the error. Using the upwind flux, the error reaches the asymptotic value faster, and to a lower value than a central flux gives, especially for low resolution computations. The differences in the error caused by the numerical flux choice decrease as the solution becomes better resolved.

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Acknowledgements

The authors would like to thank Tim Warburton for supplying the intermediate steps to his convergence proofs.

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Authors and Affiliations

  1. Department of Mathematics, The Florida State University, Tallahassee, FL, 32312, USA

    David A. Kopriva

  2. Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

    Jan Nordström

  3. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Cologne, Germany

    Gregor J. Gassner

Authors
  1. David A. Kopriva
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  2. Jan Nordström
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  3. Gregor J. Gassner
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Correspondence to David A. Kopriva.

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Kopriva, D.A., Nordström, J. & Gassner, G.J. Error Boundedness of Discontinuous Galerkin Spectral Element Approximations of Hyperbolic Problems. J Sci Comput 72, 314–330 (2017). https://doi.org/10.1007/s10915-017-0358-2

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  • DOI: https://doi.org/10.1007/s10915-017-0358-2

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