Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

Maurice S. Fabien 1 , Matthew G. Knepley 2 , and Beatrice M. Riviere 1
  • 1 Department of Computational and Applied Mathematics, Rice University, TX 77005, Houston, USA
  • 2 Department of Computer Science and Engineering, State University of New York at Buffalo, New York, 14260, Buffalo, USA
Maurice S. Fabien
  • Corresponding author
  • Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
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, Matthew G. Knepley
  • Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, New York, 14260, USA
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and Beatrice M. Riviere
  • Department of Computational and Applied Mathematics, Rice University, Houston, TX 77005, USA
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Abstract

The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

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