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Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions

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Abstract

In this paper we derive an a priori error analysis for interior penalty discontinuous Galerkin finite element discretizations of the Poisson equation with exact solution in W 2,p, p∈(1,2]. We show that the DGFEM converges at an optimal algebraic rate with respect to the number of degrees of freedom.

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Authors and Affiliations

  1. Mathematics Institute, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Thomas P. Wihler

  2. Computational and Applied Mathematics Department, Rice University, 6100 Main Street, MS-134, Houston, TX 77005-1892, USA

    Béatrice Rivière

Authors
  1. Thomas P. Wihler
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  2. Béatrice Rivière
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Correspondence to Thomas P. Wihler.

Additional information

B. Rivière research was partially supported by NSF grant DMS 0810422.

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Wihler, T.P., Rivière, B. Discontinuous Galerkin Methods for Second-Order Elliptic PDE with Low-Regularity Solutions. J Sci Comput 46, 151–165 (2011). https://doi.org/10.1007/s10915-010-9387-9

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  • DOI: https://doi.org/10.1007/s10915-010-9387-9

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