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Fourier Type Error Analysis of the Direct Discontinuous Galerkin Method and Its Variations for Diffusion Equations

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Abstract

In this paper we present Fourier type error analysis on the recent four discontinuous Galerkin methods for diffusion equations, namely the direct discontinuous Galerkin (DDG) method (Liu and Yan in SIAM J. Numer. Anal. 47(1):475–698, 2009); the DDG method with interface corrections (Liu and Yan in Commun. Comput. Phys. 8(3):541–564, 2010); and the DDG method with symmetric structure (Vidden and Yan in SIAM J. Numer. Anal., 2011); and a DG method with nonsymmetric structure (Yan, A discontinuous Galerkin method for nonlinear diffusion problems with nonsymmetric structure, 2011). The Fourier type L 2 error analysis demonstrates the optimal convergence of the four DG methods with suitable numerical fluxes. The theoretical predicted errors agree well with the numerical results.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China

    Mengping Zhang

  2. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Jue Yan

Authors
  1. Mengping Zhang
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  2. Jue Yan
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Correspondence to Jue Yan.

Additional information

The research of M. Zhang is supported by NSFC grant 11071234 and 91024025.

The research of J. Yan is supported by NSF grant DMS-0915247.

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Zhang, M., Yan, J. Fourier Type Error Analysis of the Direct Discontinuous Galerkin Method and Its Variations for Diffusion Equations. J Sci Comput 52, 638–655 (2012). https://doi.org/10.1007/s10915-011-9564-5

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  • DOI: https://doi.org/10.1007/s10915-011-9564-5

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