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Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case

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In this paper we analyze a family of discontinuous Galerkin methods, parameterized by two real parameters, for elliptic problems in one dimension. Our main results are: (1) a complete inf-sup stability analysis characterizing the parameter values yielding a stable scheme and energy norm error estimates as a direct consequence thereof, (2) an analysis of the error in L2 where the standard duality argument only works for special parameter values yielding a symmetric bilinear form and different orders of convergence are obtained for odd and even order polynomials in the nonsymmetric case. The analysis is consistent with numerical results and similar behavior is observed in two dimensions.

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Authors and Affiliations

  1. Department of Mathematics, Chalmers University of Technology, 41296, Göteborg, Sweden

    Mats G. Larson

  2. Department of Applied Mechanics, Chalmers University of Technology, 412 96, Göteborg, Sweden

    A. Jonas Niklasson

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  1. Mats G. Larson
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  2. A. Jonas Niklasson
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Correspondence to Mats G. Larson.

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Mathematics Subject Classification (2000): 65M60, 65M15

Research supported by: The Swedish Foundation for International Cooperation in Research and Higher Education

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Larson, M., Niklasson, A. Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case. Numer. Math. 99, 113–130 (2004). https://doi.org/10.1007/s00211-004-0528-7

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  • DOI: https://doi.org/10.1007/s00211-004-0528-7

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