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Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations

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Abstract

We numerically verify that the non-symmetric interior penalty Galerkin method and the Oden-Babus̆ka-Baumann method have sub-optimal convergence properties when measured in the L 2-norm for odd polynomial approximations. We provide numerical examples that use piece-wise linear and cubic polynomials to approximate a second-order elliptic problem in one and two dimensions.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02906, USA

    Johnny Guzmán

  2. Department of Computational and Applied Mathematics, Rice University, Houston, TX, 77005, USA

    Béatrice Rivière

Authors
  1. Johnny Guzmán
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  2. Béatrice Rivière
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Correspondence to Johnny Guzmán.

Additional information

The first author was supported by an NSF Postdoctoral Fellowship.

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Guzmán, J., Rivière, B. Sub-optimal Convergence of Non-symmetric Discontinuous Galerkin Methods for Odd Polynomial Approximations. J Sci Comput 40, 273–280 (2009). https://doi.org/10.1007/s10915-008-9255-z

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  • DOI: https://doi.org/10.1007/s10915-008-9255-z

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