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Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems

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Abstract

Fourier continuation (FC) is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier expansions. These methods have been used in partial differential equation (PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical experiments. Discontinuous Galerkin (DG) methods are increasingly used for solving PDEs and, as all Galerkin formulations, come with a strong framework for proving the stability and the convergence. Here we propose the use of FC in forming a new basis for the DG framework.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, USA

    Kiera van der Sande

  2. Department of Computational Mathematics, Science & Engineering, Michigan State University, East Lansing, USA

    Daniel Appelö

  3. Department of Mathematics, Michigan State University, East Lansing, USA

    Daniel Appelö

  4. Department of Mathematics, Kansas State University, Manhattan, KS, USA

    Nathan Albin

Authors
  1. Kiera van der Sande
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  2. Daniel Appelö
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  3. Nathan Albin
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Correspondence to Daniel Appelö.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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This work was supported by the National Science Foundation Grant DMS-1913076. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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van der Sande, K., Appelö, D. & Albin, N. Fourier Continuation Discontinuous Galerkin Methods for Linear Hyperbolic Problems. Commun. Appl. Math. Comput. 5, 1385–1405 (2023). https://doi.org/10.1007/s42967-022-00205-1

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  • DOI: https://doi.org/10.1007/s42967-022-00205-1

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